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Question
Write the value of cos−1 (cos 1540°).
Solution
We know that
\[\cos^{- 1} \left( cosx \right) = x\]
Now,
\[\cos^{- 1} \left( \cos {1540}^\circ \right) = \cos^{- 1} \left\{ \cos\left( 1440 + {100}^\circ \right) \right\}\]
\[ = \cos^{- 1} \left\{ \cos\left( {100}^\circ \right) \right\} \left[ \because \cos\left( 4\pi + {100}^\circ \right) = \cos{100}^\circ \right]\]
\[ = {100}^\circ\]
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