Question

Write the value of cos⁻¹ (cos 1540°).

Answer 1

We know that 

\[\cos^{- 1} \left( cosx \right) = x\]

Now,

\[\cos^{- 1} \left( \cos {1540}^\circ \right) = \cos^{- 1} \left\{ \cos\left( 1440 + {100}^\circ \right) \right\}\]
\[ = \cos^{- 1} \left\{ \cos\left( {100}^\circ \right) \right\} \left[ \because \cos\left( 4\pi + {100}^\circ \right) = \cos{100}^\circ \right]\]
\[ = {100}^\circ\]