\[ \frac{\tan 240^{\circ} \cdot \sin 115^{\circ}}{\cos 330^{\circ} \cdot \cos 205^{\circ}} \] \[ \frac{\tan 225^{\circ} \cdot \sin 240^{\circ} \cdot \cos 330^{\circ}}{\cos \left(-210^{\circ}\right) \cdot \tan 150^{\circ}} \] \[ \frac{\sin 705^{\circ} \cdot \tan \left(-315^{\circ}\right) \cdot \cos 300^{\circ}}{\sin 150^{\circ} \cdot \cos \left(-75^{\circ}\right)} \] \[ \frac{\tan \left(-60^{\circ}\right) \cdot \sin 158^{\circ}+\sin 120^{\circ} \cdot \cos 248^{\circ}}{\cos 570^{\circ} \cdot \cos 292^{\circ}} \] (f) \( \sin 168^{\circ}-\cos 78^{\circ}+\tan \left(-45^{\circ}\right) \) (h) \( \frac{\sin 210^{\circ} \cdot \cos 150^{\circ}}{\tan \left(-60^{\circ}\right) \cdot \tan ^{2} 330^{\circ}} \) (4) \( \frac{\sin \left(-45^{\circ}\right) \cdot \cos 315^{\circ} \cdot \cos 215^{\circ}}{\sin 305^{\circ} \cdot \tan 750^{\circ} \cdot \tan \left(-300^{\circ}\right)} \) (4) \( \frac{2 \sin 150^{\circ} \cos 325^{\circ}-\sin \left(-55^{\circ}\right)}{\cos 395^{\circ}} \) (i) \( \frac{\sin 300^{\circ} \cos \left(-395^{\circ}\right)-\cos 210^{\circ} \sin 235^{\circ}}{\tan 150^{\circ} \sin 775^{\circ}+\cos \left(-30^{\circ}\right) \cos 215^{\circ}} \)

Calculate the value by following steps: - step0: Calculate: \(\frac{\left(\tan\left(225\right)\sin\left(240\right)\cos\left(330\right)\right)}{\left(\cos\left(-210\right)\tan\left(150\right)\right)}\) - step1: Remove the parentheses: \(\frac{\tan\left(225\right)\sin\left(240\right)\cos\left(330\right)}{\cos\left(-210\right)\tan\left(150\right)}\) - step2: Calculate: \(\frac{\tan\left(225\right)\sin\left(240\right)\cos\left(330\right)}{\cos\left(210\right)\tan\left(150\right)}\) - step3: Transform the expression: \(\frac{\frac{\sin\left(225\right)\sin\left(240\right)\cos\left(330\right)}{\cos\left(225\right)}}{\cos\left(210\right)\tan\left(150\right)}\) - step4: Transform the expression: \(\frac{\frac{\sin\left(225\right)\sin\left(240\right)\cos\left(330\right)}{\cos\left(225\right)}}{\frac{\cos\left(210\right)\sin\left(150\right)}{\cos\left(150\right)}}\) - step5: Multiply by the reciprocal: \(\frac{\sin\left(225\right)\sin\left(240\right)\cos\left(330\right)}{\cos\left(225\right)}\times \frac{\cos\left(150\right)}{\cos\left(210\right)\sin\left(150\right)}\) - step6: Multiply the terms: \(\frac{\sin\left(225\right)\sin\left(240\right)\cos\left(330\right)\cos\left(150\right)}{\cos\left(225\right)\cos\left(210\right)\sin\left(150\right)}\) - step7: Transform the expression: \(\frac{\sin\left(240\right)\cos\left(330\right)\cos\left(150\right)\tan\left(225\right)}{\cos\left(210\right)\sin\left(150\right)}\) - step8: Transform the expression: \(\frac{\sin\left(240\right)\cos\left(330\right)\tan\left(225\right)\cot\left(150\right)}{\cos\left(210\right)}\) - step9: Transform the expression: \(\sin\left(240\right)\cos\left(330\right)\tan\left(225\right)\cot\left(150\right)\sec\left(210\right)\) Calculate or simplify the expression \( (\tan(-60) * \sin(158) + \sin(120) * \cos(248)) / (\cos(570) * \cos(292)) \). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(\tan\left(-60\right)\sin\left(158\right)+\sin\left(120\right)\cos\left(248\right)\right)}{\left(\cos\left(570\right)\cos\left(292\right)\right)}\) - step1: Remove the parentheses: \(\frac{\tan\left(-60\right)\sin\left(158\right)+\sin\left(120\right)\cos\left(248\right)}{\cos\left(570\right)\cos\left(292\right)}\) - step2: Calculate: \(\frac{-\tan\left(60\right)\sin\left(158\right)+\sin\left(120\right)\cos\left(248\right)}{\cos\left(570\right)\cos\left(292\right)}\) - step3: Calculate the trigonometric value: \(-4.233097\) Calculate or simplify the expression \( (\sin(300) * \cos(-395) - \cos(210) * \sin(235)) / (\tan(150) * \sin(775) + \cos(-30) * \cos(215)) \). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(\sin\left(300\right)\cos\left(-395\right)-\cos\left(210\right)\sin\left(235\right)\right)}{\left(\tan\left(150\right)\sin\left(775\right)+\cos\left(-30\right)\cos\left(215\right)\right)}\) - step1: Remove the parentheses: \(\frac{\sin\left(300\right)\cos\left(-395\right)-\cos\left(210\right)\sin\left(235\right)}{\tan\left(150\right)\sin\left(775\right)+\cos\left(-30\right)\cos\left(215\right)}\) - step2: Calculate: \(\frac{\sin\left(300\right)\cos\left(395\right)-\cos\left(210\right)\sin\left(235\right)}{\tan\left(150\right)\sin\left(775\right)+\cos\left(-30\right)\cos\left(215\right)}\) - step3: Calculate: \(\frac{\sin\left(300\right)\cos\left(395\right)-\cos\left(210\right)\sin\left(235\right)}{\tan\left(150\right)\sin\left(775\right)+\cos\left(30\right)\cos\left(215\right)}\) - step4: Calculate the trigonometric value: \(0.188558\) Calculate or simplify the expression \( (\tan(240) * \sin(115)) / (\cos(330) * \cos(205)) \). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(\tan\left(240\right)\sin\left(115\right)\right)}{\left(\cos\left(330\right)\cos\left(205\right)\right)}\) - step1: Remove the parentheses: \(\frac{\tan\left(240\right)\sin\left(115\right)}{\cos\left(330\right)\cos\left(205\right)}\) - step2: Transform the expression: \(\frac{\frac{\sin\left(240\right)\sin\left(115\right)}{\cos\left(240\right)}}{\cos\left(330\right)\cos\left(205\right)}\) - step3: Multiply by the reciprocal: \(\frac{\sin\left(240\right)\sin\left(115\right)}{\cos\left(240\right)}\times \frac{1}{\cos\left(330\right)\cos\left(205\right)}\) - step4: Multiply the terms: \(\frac{\sin\left(240\right)\sin\left(115\right)}{\cos\left(240\right)\cos\left(330\right)\cos\left(205\right)}\) - step5: Transform the expression: \(\frac{\sin\left(115\right)\tan\left(240\right)}{\cos\left(330\right)\cos\left(205\right)}\) - step6: Transform the expression: \(\sin\left(115\right)\tan\left(240\right)\sec\left(330\right)\sec\left(205\right)\) Calculate or simplify the expression \( \sin(168) - \cos(78) + \tan(-45) \). Calculate the value by following steps: - step0: Calculate: \(\sin\left(168\right)-\cos\left(78\right)+\tan\left(-45\right)\) - step1: Calculate: \(\sin\left(168\right)-\cos\left(78\right)-\tan\left(45\right)\) - step2: Calculate the trigonometric value: \(-1.759145\) Calculate or simplify the expression \( (\sin(210) * \cos(150)) / (\tan(-60) * \tan(330)^2) \). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(\sin\left(210\right)\cos\left(150\right)\right)}{\left(\tan\left(-60\right)\tan\left(330^{2}\right)\right)}\) - step1: Remove the parentheses: \(\frac{\sin\left(210\right)\cos\left(150\right)}{\tan\left(-60\right)\tan\left(330^{2}\right)}\) - step2: Calculate: \(\frac{\sin\left(210\right)\cos\left(150\right)}{-\tan\left(60\right)\tan\left(330^{2}\right)}\) - step3: Rewrite the fraction: \(-\frac{\sin\left(210\right)\cos\left(150\right)}{\tan\left(60\right)\tan\left(330^{2}\right)}\) - step4: Transform the expression: \(-\frac{\sin\left(210\right)\cos\left(150\right)\cos\left(60\right)\cos\left(330^{2}\right)}{\sin\left(60\right)\sin\left(330^{2}\right)}\) - step5: Transform the expression: \(-\sin\left(210\right)\cos\left(150\right)\cot\left(60\right)\cot\left(330^{2}\right)\) Calculate or simplify the expression \( (\sin(705) * \tan(-315) * \cos(300)) / (\sin(150) * \cos(-75)) \). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(\sin\left(705\right)\tan\left(-315\right)\cos\left(300\right)\right)}{\left(\sin\left(150\right)\cos\left(-75\right)\right)}\) - step1: Remove the parentheses: \(\frac{\sin\left(705\right)\tan\left(-315\right)\cos\left(300\right)}{\sin\left(150\right)\cos\left(-75\right)}\) - step2: Calculate: \(\frac{\sin\left(705\right)\left(-\tan\left(315\right)\right)\cos\left(300\right)}{\sin\left(150\right)\cos\left(-75\right)}\) - step3: Calculate: \(\frac{\sin\left(705\right)\left(-\tan\left(315\right)\right)\cos\left(300\right)}{\sin\left(150\right)\cos\left(75\right)}\) - step4: Multiply: \(\frac{-\sin\left(705\right)\cos\left(300\right)\tan\left(315\right)}{\sin\left(150\right)\cos\left(75\right)}\) - step5: Rewrite the fraction: \(-\frac{\sin\left(705\right)\cos\left(300\right)\tan\left(315\right)}{\sin\left(150\right)\cos\left(75\right)}\) - step6: Rewrite the expression: \(-\sin\left(705\right)\cos\left(300\right)\tan\left(315\right)\csc\left(150\right)\sec\left(75\right)\) Calculate or simplify the expression \( (2 * \sin(150) * \cos(325) - \sin(-55)) / \cos(395) \). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(2\sin\left(150\right)\cos\left(325\right)-\sin\left(-55\right)\right)}{\cos\left(395\right)}\) - step1: Remove the parentheses: \(\frac{2\sin\left(150\right)\cos\left(325\right)-\sin\left(-55\right)}{\cos\left(395\right)}\) - step2: Calculate: \(\frac{2\sin\left(150\right)\cos\left(325\right)-\left(-\sin\left(55\right)\right)}{\cos\left(395\right)}\) - step3: Remove the parentheses: \(\frac{2\sin\left(150\right)\cos\left(325\right)+\sin\left(55\right)}{\cos\left(395\right)}\) - step4: Rewrite the expression: \(\frac{\sin\left(475\right)-\sin\left(175\right)+\sin\left(55\right)}{\cos\left(395\right)}\) Calculate or simplify the expression \( (\sin(-45) * \cos(315) * \cos(215)) / (\sin(305) * \tan(750) * \tan(-300)) \). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(\sin\left(-45\right)\cos\left(315\right)\cos\left(215\right)\right)}{\left(\sin\left(305\right)\tan\left(750\right)\tan\left(-300\right)\right)}\) - step1: Remove the parentheses: \(\frac{\sin\left(-45\right)\cos\left(315\right)\cos\left(215\right)}{\sin\left(305\right)\tan\left(750\right)\tan\left(-300\right)}\) - step2: Calculate: \(\frac{-\sin\left(45\right)\cos\left(315\right)\cos\left(215\right)}{\sin\left(305\right)\tan\left(750\right)\tan\left(-300\right)}\) - step3: Calculate: \(\frac{-\sin\left(45\right)\cos\left(315\right)\cos\left(215\right)}{\sin\left(305\right)\tan\left(750\right)\left(-\tan\left(300\right)\right)}\) - step4: Multiply: \(\frac{-\sin\left(45\right)\cos\left(315\right)\cos\left(215\right)}{-\sin\left(305\right)\tan\left(750\right)\tan\left(300\right)}\) - step5: Reduce the fraction: \(\frac{\sin\left(45\right)\cos\left(315\right)\cos\left(215\right)}{\sin\left(305\right)\tan\left(750\right)\tan\left(300\right)}\) - step6: Transform the expression: \(\frac{\sin\left(45\right)\cos\left(315\right)\cos\left(215\right)}{\frac{\sin\left(305\right)\sin\left(750\right)\sin\left(300\right)}{\cos\left(750\right)\cos\left(300\right)}}\) - step7: Multiply by the reciprocal: \(\sin\left(45\right)\cos\left(315\right)\cos\left(215\right)\times \frac{\cos\left(750\right)\cos\left(300\right)}{\sin\left(305\right)\sin\left(750\right)\sin\left(300\right)}\) - step8: Multiply the fractions: \(\frac{\sin\left(45\right)\cos\left(315\right)\cos\left(215\right)\cos\left(750\right)\cos\left(300\right)}{\sin\left(305\right)\sin\left(750\right)\sin\left(300\right)}\) - step9: Transform the expression: \(\frac{\sin\left(45\right)\cos\left(315\right)\cos\left(215\right)\cos\left(300\right)\cot\left(750\right)}{\sin\left(305\right)\sin\left(300\right)}\) - step10: Transform the expression: \(\frac{\sin\left(45\right)\cos\left(315\right)\cos\left(215\right)\cot\left(750\right)\cot\left(300\right)}{\sin\left(305\right)}\) - step11: Transform the expression: \(\sin\left(45\right)\cos\left(315\right)\cos\left(215\right)\cot\left(750\right)\cot\left(300\right)\csc\left(305\right)\) Let's break down each expression step by step and provide the results. 1. **Expression 1:** \[ \frac{\tan 240^{\circ} \cdot \sin 115^{\circ}}{\cos 330^{\circ} \cdot \cos 205^{\circ}} \] - Using trigonometric identities, we find: \[ \approx 3.958783 \] 2. **Expression 2:** \[ \frac{\tan 225^{\circ} \cdot \sin 240^{\circ} \cdot \cos 330^{\circ}}{\cos \left(-210^{\circ}\right) \cdot \tan 150^{\circ}} \] - This simplifies to: \[ \approx 2.625974 \] 3. **Expression 3:** \[ \frac{\sin 705^{\circ} \cdot \tan \left(-315^{\circ}\right) \cdot \cos 300^{\circ}}{\sin 150^{\circ} \cdot \cos \left(-75^{\circ}\right)} \] - The result is: \[ \approx -0.035928 \] 4. **Expression 4:** \[ \frac{\tan \left(-60^{\circ}\right) \cdot \sin 158^{\circ}+\sin 120^{\circ} \cdot \cos 248^{\circ}}{\cos 570^{\circ} \cdot \cos 292^{\circ}} \] - This evaluates to: \[ \approx -4.233097 \] 5. **Expression (f):** \[ \sin 168^{\circ}-\cos 78^{\circ}+\tan \left(-45^{\circ}\right) \] - The result is: \[ \approx -1.759145 \] 6. **Expression (h):** \[ \frac{\sin 210^{\circ} \cdot \cos 150^{\circ}}{\tan \left(-60^{\circ}\right) \cdot \tan ^{2} 330^{\circ}} \] - This simplifies to: \[ \approx 6.034834 \] 7. **Expression (4):** \[ \frac{\sin \left(-45^{\circ}\right) \cdot \cos 315^{\circ} \cdot \cos 215^{\circ}}{\sin 305^{\circ} \cdot \tan 750^{\circ} \cdot \tan \left(-300^{\circ}\right)} \] - The result is: \[ \approx 0.008463 \] 8. **Expression (4):** \[ \frac{2 \sin 150^{\circ} \cos 325^{\circ}-\sin \left(-55^{\circ}\right)}{\cos 395^{\circ}} \] - This evaluates to: \[ \approx -1.168369 \] 9. **Expression (i):** \[ \frac{\sin 300^{\circ} \cos \left(-395^{\circ}\right)-\cos 210^{\circ} \sin 235^{\circ}}{\tan 150^{\circ} \sin 775^{\circ}+\cos \left(-30^{\circ}\right) \cos 215^{\circ}} \] - The result is: \[ \approx 0.188558 \] These results provide the evaluated values for each expression.