Questions Discussed:
Evaluate each of the following:
Question 1. { \displaystyle {{\sin }^{-1}}\left( -\frac{\sqrt{3}}{2} \right) }
Question 2. { \displaystyle {{\cot }^{-1}}\left( \frac{-1}{\sqrt{3}} \right) }
Question 3. { \displaystyle {{\tan }^{-1}}\left( -\frac{1}{\sqrt{3}} \right) }
Question 4. { \displaystyle {{\tan }^{-1}}(1)}+{ \displaystyle{{\cos }^{-1}}\left( -\frac{1}{2} \right)}+{ \displaystyle{{\sin }^{-1}}\left( -\frac{1}{2} \right) }
Question 5. { \displaystyle {{\cos }^{-1}}\left( \frac{1}{2} \right)}+{ \displaystyle2{{\sin }^{-1}}\left( \frac{1}{2} \right) }
Question 6. { \displaystyle {{\tan }^{-1}}\sqrt{3}-{{\sec }^{-1}}(-2) }
Question 7. { \displaystyle {{\sin }^{-1}}\left( \sin \frac{4\pi }{5} \right) }
Question 8. { \displaystyle {{\sin }^{-1}}\left( \sin \frac{2\pi }{3} \right) }
Question 9. { \displaystyle {{\tan }^{-1}}\left( \tan \frac{3\pi }{4} \right) }
Question 10 { \displaystyle {{\cos }^{-1}}\left( \cos \frac{7\pi }{6} \right) }
Question 11 { \displaystyle \sin \left( \frac{\pi }{3}-{{\sin }^{-1}}\left( -\frac{1}{2} \right) \right) }
Question 12 { \displaystyle {{\tan }^{-1}}\sqrt{3}-{{\cot }^{-1}}(-\sqrt{3}) }
Question 13 { \displaystyle {{\csc }^{-1}}(-2) }
Question 14 { \displaystyle {{\sin }^{-1}}\left( \sin \frac{3\pi }{5} \right) }
Question 16 { \displaystyle {{\cos }^{-1}}\left( \cos \frac{13\pi }{6} \right) }
Question 17 { \displaystyle {{\tan }^{-1}}\left( \tan \frac{7\pi }{6} \right) }
Question 18 { \displaystyle {{\cos }^{-1}}[\cos (-680{}^\circ )] }
Question 20 { \displaystyle {{\tan }^{-1}}\left( \tan \frac{5\pi }{6} \right) }