Question

Write the value of cos⁻¹ \[\left( \cos\frac{5\pi}{4} \right)\]

Answer 1

\[\cos^{- 1} \left( \cos\frac{5\pi}{4} \right) \neq \frac{5\pi}{4}\]as
\[\frac{5\pi}{4}\]  does not lie between 0 and π
We have
\[\cos^{- 1} \left( \cos\frac{5\pi}{4} \right) = \cos^{- 1} \left\{ \cos\left( 2\pi - \frac{3\pi}{4} \right) \right\}\]
\[ = \cos^{- 1} \left\{ \cos\left( \frac{3\pi}{4} \right) \right\}\]
\[ = \frac{3\pi}{4}\]