2. Simpilty the expresston tally \( 0_{0}^{0} \frac{\sin 698^{\circ} \cdot \cos 300^{\circ}}{\tan 133^{\circ} \cdot \cos (-248)^{\circ}} \)

Rewrite the angle by following steps: - step0: Convert to radians: \(133^{\circ}\) - step1: Convert to radians: \(\frac{133\pi }{180}\) Rewrite the number \( -248^{\circ} \). Rewrite the angle by following steps: - step0: Convert to radians: \(-248^{\circ}\) - step1: Convert to radians: \(-\frac{62\pi }{45}\) Rewrite the number \( 300^{\circ} \). Rewrite the angle by following steps: - step0: Convert to radians: \(300^{\circ}\) - step1: Convert to radians: \(\frac{5\pi }{3}\) Rewrite the number \( 698^{\circ} \). Rewrite the angle by following steps: - step0: Convert to radians: \(698^{\circ}\) - step1: Convert to radians: \(\frac{349\pi }{90}\) Calculate or simplify the expression \( \frac{\sin \left(\frac{349\pi }{90}\right) \cdot \cos \left(\frac{5\pi }{3}\right)}{\tan \left(\frac{133\pi }{180}\right) \cdot \cos \left(-\frac{62\pi }{45}\right)} \). Calculate the value by following steps: - step0: Calculate: \(\frac{\sin\left(\frac{349\pi }{90}\right)\cos\left(\frac{5\pi }{3}\right)}{\tan\left(\frac{133\pi }{180}\right)\cos\left(-\frac{62\pi }{45}\right)}\) - step1: Calculate: \(\frac{\sin\left(\frac{169\pi }{90}\right)\cos\left(\frac{5\pi }{3}\right)}{\tan\left(\frac{133\pi }{180}\right)\cos\left(-\frac{62\pi }{45}\right)}\) - step2: Calculate: \(\frac{\sin\left(\frac{169\pi }{90}\right)\cos\left(\frac{5\pi }{3}\right)}{\tan\left(\frac{133\pi }{180}\right)\cos\left(\frac{62\pi }{45}\right)}\) - step3: Multiply the terms: \(\frac{\frac{\sin\left(\frac{169\pi }{90}\right)}{2}}{\tan\left(\frac{133\pi }{180}\right)\cos\left(\frac{62\pi }{45}\right)}\) - step4: Calculate the trigonometric value: \(\frac{\frac{\sin\left(\frac{169\pi }{90}\right)}{2}}{-\tan\left(\frac{47\pi }{180}\right)\cos\left(\frac{62\pi }{45}\right)}\) - step5: Multiply by the reciprocal: \(\frac{\sin\left(\frac{169\pi }{90}\right)}{2}\left(-\frac{1}{\tan\left(\frac{47\pi }{180}\right)\cos\left(\frac{62\pi }{45}\right)}\right)\) - step6: Multiply the numbers: \(-\frac{\sin\left(\frac{169\pi }{90}\right)}{2}\times \frac{1}{\tan\left(\frac{47\pi }{180}\right)\cos\left(\frac{62\pi }{45}\right)}\) - step7: Reduce the numbers: \(-\frac{1}{2}\times \frac{1}{\tan\left(\frac{47\pi }{180}\right)}\) - step8: Multiply the fractions: \(-\frac{1}{2\tan\left(\frac{47\pi }{180}\right)}\) - step9: Transform the expression: \(-\frac{\cos\left(\frac{47\pi }{180}\right)}{2\sin\left(\frac{47\pi }{180}\right)}\) - step10: Transform the expression: \(-\frac{\cot\left(\frac{47\pi }{180}\right)}{2}\) To simplify the expression \[ 0_{0}^{0} \frac{\sin 698^{\circ} \cdot \cos 300^{\circ}}{\tan 133^{\circ} \cdot \cos (-248)^{\circ}}, \] we follow these steps: 1. **Convert angles to radians:** - \( 698^{\circ} = \frac{349\pi}{90} \) - \( 300^{\circ} = \frac{5\pi}{3} \) - \( 133^{\circ} = \frac{133\pi}{180} \) - \( -248^{\circ} = -\frac{62\pi}{45} \) 2. **Substituting the angles into the expression:** The expression becomes: \[ \frac{\sin \left(\frac{349\pi}{90}\right) \cdot \cos \left(\frac{5\pi}{3}\right)}{\tan \left(\frac{133\pi}{180}\right) \cdot \cos \left(-\frac{62\pi}{45}\right)}. \] 3. **Simplifying the expression:** After performing the calculations, we find that the simplified form of the expression is: \[ -\frac{\cot\left(\frac{47\pi}{180}\right)}{2}. \] Thus, the final simplified expression is \[ -\frac{\cot\left(\frac{47\pi}{180}\right)}{2}. \]