Properties of inverse trigonometric function
\[sin^{-1}(-x)=-sin^{-1}(x)\]
\[ cos^{-1}(-x)=\pi -cos^{-1}(x)\]
\[ tan^{-1}(-x)=-tan^{-1}(x)\]
\[ cosec^{-1}(-x)=-cosec^{-1}(x)\]
\[ sec^{-1}(-x)=\pi -sec^{-1}(x)\]
\[ cot^{-1}(-x)=-cot^{-1}(x)\]
Properties of complementary angle
\[ sin(\frac{\pi }{2}-x)=cosx\]
\[cos(\frac{\pi }{2}-x)=sinx\]
\[tan(\frac{\pi }{2}-x)=cotx\]
\[cosec(\frac{\pi }{2}-x)=secx\]
\[sec(\frac{\pi }{2}-x)=cosecx\]
Calculation on invere function
\[sin(\frac{\pi }{2}-sin^{-1}(-\frac{\sqrt{3}}{2}))\]
\[sin(\frac{\pi }{2}+sin^{-1}(\frac{\sqrt{3}}{2}))\]
\[sin(\frac{5\pi }{6})\]=\[ \frac{1}{2}\]
