9)) \( \frac{\cos 30^{\circ} \sin 45^{\circ} \tan 60^{\circ} \cos 45^{\circ}}{\sin 60 \tan 30} \quad \) 10) \( \left(\tan 60^{\circ}\right)^{2}+\frac{\cos 60^{\circ}}{\sqrt{3}}+\frac{\sin 45^{\circ}}{\sqrt{2}} \)

Calculate the value by following steps: - step0: Calculate: \(\tan^{2}\left(60\right)+\left(\frac{\cos\left(60\right)}{\sqrt{3}}\right)+\left(\frac{\sin\left(45\right)}{\sqrt{2}}\right)\) - step1: Remove the parentheses: \(\tan^{2}\left(60\right)+\frac{\cos\left(60\right)}{\sqrt{3}}+\left(\frac{\sin\left(45\right)}{\sqrt{2}}\right)\) - step2: Remove the parentheses: \(\tan^{2}\left(60\right)+\frac{\cos\left(60\right)}{\sqrt{3}}+\frac{\sin\left(45\right)}{\sqrt{2}}\) - step3: Add the terms: \(\tan^{2}\left(60\right)+\frac{\sqrt{2}\times \cos\left(60\right)+\sqrt{3}\times \sin\left(45\right)}{\sqrt{6}}\) - step4: Reduce fractions to a common denominator: \(\frac{\tan^{2}\left(60\right)\times \sqrt{6}}{\sqrt{6}}+\frac{\sqrt{2}\times \cos\left(60\right)+\sqrt{3}\times \sin\left(45\right)}{\sqrt{6}}\) - step5: Transform the expression: \(\frac{\tan^{2}\left(60\right)\times \sqrt{6}+\sqrt{2}\times \cos\left(60\right)+\sqrt{3}\times \sin\left(45\right)}{\sqrt{6}}\) - step6: Reorder the terms: \(\frac{\sqrt{6}\times \tan^{2}\left(60\right)+\sqrt{2}\times \cos\left(60\right)+\sqrt{3}\times \sin\left(45\right)}{\sqrt{6}}\) - step7: Calculate the trigonometric value: \(0.15423\) Calculate or simplify the expression \( (\cos(30) * \sin(45) * \tan(60) * \cos(45)) / (\sin(60) * \tan(30)) \). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(\cos\left(30\right)\sin\left(45\right)\tan\left(60\right)\cos\left(45\right)\right)}{\left(\sin\left(60\right)\tan\left(30\right)\right)}\) - step1: Remove the parentheses: \(\frac{\cos\left(30\right)\sin\left(45\right)\tan\left(60\right)\cos\left(45\right)}{\sin\left(60\right)\tan\left(30\right)}\) - step2: Transform the expression: \(\frac{\frac{\cos\left(30\right)\sin\left(45\right)\cos\left(45\right)\sin\left(60\right)}{\cos\left(60\right)}}{\sin\left(60\right)\tan\left(30\right)}\) - step3: Transform the expression: \(\frac{\frac{\cos\left(30\right)\sin\left(45\right)\cos\left(45\right)\sin\left(60\right)}{\cos\left(60\right)}}{\frac{\sin\left(60\right)\sin\left(30\right)}{\cos\left(30\right)}}\) - step4: Multiply by the reciprocal: \(\frac{\cos\left(30\right)\sin\left(45\right)\cos\left(45\right)\sin\left(60\right)}{\cos\left(60\right)}\times \frac{\cos\left(30\right)}{\sin\left(60\right)\sin\left(30\right)}\) - step5: Reduce the fraction: \(\frac{\cos\left(30\right)\sin\left(45\right)\cos\left(45\right)}{\cos\left(60\right)}\times \frac{\cos\left(30\right)}{\sin\left(30\right)}\) - step6: Multiply the terms: \(\frac{\cos\left(30\right)\sin\left(45\right)\cos\left(45\right)\cos\left(30\right)}{\cos\left(60\right)\sin\left(30\right)}\) - step7: Multiply the terms: \(\frac{\cos^{2}\left(30\right)\sin\left(45\right)\cos\left(45\right)}{\cos\left(60\right)\sin\left(30\right)}\) - step8: Transform the expression: \(\cos^{2}\left(30\right)\sin\left(45\right)\cos\left(45\right)\sec\left(60\right)\csc\left(30\right)\) - step9: Simplify: \(\sin\left(45\right)\cos\left(45\right)\sec\left(60\right)\csc\left(30\right)\cos^{2}\left(30\right)\) เรามาแก้ปัญหาทั้งสองข้อกันทีละขั้นตอน: ### ข้อ 9 เราต้องคำนวณค่า: \[ \frac{\cos 30^{\circ} \sin 45^{\circ} \tan 60^{\circ} \cos 45^{\circ}}{\sin 60^{\circ} \tan 30^{\circ}} \] 1. **หาค่าต่าง ๆ**: - \(\cos 30^{\circ} = \frac{\sqrt{3}}{2}\) - \(\sin 45^{\circ} = \frac{\sqrt{2}}{2}\) - \(\tan 60^{\circ} = \sqrt{3}\) - \(\cos 45^{\circ} = \frac{\sqrt{2}}{2}\) - \(\sin 60^{\circ} = \frac{\sqrt{3}}{2}\) - \(\tan 30^{\circ} = \frac{1}{\sqrt{3}}\) 2. **แทนค่าลงในสมการ**: \[ \frac{\left(\frac{\sqrt{3}}{2}\right) \left(\frac{\sqrt{2}}{2}\right) \left(\sqrt{3}\right) \left(\frac{\sqrt{2}}{2}\right)}{\left(\frac{\sqrt{3}}{2}\right) \left(\frac{1}{\sqrt{3}}\right)} \] 3. **คำนวณ**: - ตัวเศษ: \[ \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{2}}{2} \cdot \sqrt{3} \cdot \frac{\sqrt{2}}{2} = \frac{3 \cdot 2}{4} = \frac{3}{2} \] - ตัวส่วน: \[ \frac{\sqrt{3}}{2} \cdot \frac{1}{\sqrt{3}} = \frac{1}{2} \] 4. **ผลลัพธ์**: \[ \frac{\frac{3}{2}}{\frac{1}{2}} = 3 \] ### ข้อ 10 เราต้องคำนวณค่า: \[ \left(\tan 60^{\circ}\right)^{2}+\frac{\cos 60^{\circ}}{\sqrt{3}}+\frac{\sin 45^{\circ}}{\sqrt{2}} \] 1. **หาค่าต่าง ๆ**: - \(\tan 60^{\circ} = \sqrt{3}\) - \(\cos 60^{\circ} = \frac{1}{2}\) - \(\sin 45^{\circ} = \frac{\sqrt{2}}{2}\) 2. **แทนค่าลงในสมการ**: \[ (\sqrt{3})^{2} + \frac{\frac{1}{2}}{\sqrt{3}} + \frac{\frac{\sqrt{2}}{2}}{\sqrt{2}} \] 3. **คำนวณ**: - \((\sqrt{3})^{2} = 3\) - \(\frac{\frac{1}{2}}{\sqrt{3}} = \frac{1}{2\sqrt{3}}\) - \(\frac{\frac{\sqrt{2}}{2}}{\sqrt{2}} = \frac{1}{2}\) 4. **รวมผลลัพธ์**: \[ 3 + \frac{1}{2\sqrt{3}} + \frac{1}{2} \] 5. **ผลลัพธ์**: - คำนวณค่าโดยรวม: \[ 3 + 0.15423 \approx 3.15423 \] ### สรุปผลลัพธ์ - ข้อ 9: \(3\) - ข้อ 10: \(3.15423\)