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Question
Write the value of cos−1 (cos 350°) − sin−1 (sin 350°)
Solution
\[\cos^{- 1} \left( \cos {350}^\circ \right) - \sin^{- 1} \left( \sin {350}^\circ \right)\]
\[ = \cos^{- 1} \left\{ \cos\left( {360}^\circ - {350}^\circ \right) \right\} - \sin^{- 1} \left\{ \sin\left( {360}^\circ - {350}^\circ \right) \right\} \left[ \because \sin\left( {360}^\circ - x \right) = - \sin{x} , \cos\left( {360}^\circ - x \right) = \cos{x} \right]\]
\[ \]
\[ = \cos^{- 1} \left\{ \cos\left( {10}^\circ \right) \right\} - \sin^{- 1} \left\{ \sin\left( - {10}^\circ \right) \right\}\]
\[ = {10}^\circ - \left( - {10}^\circ \right)\]
\[ = {20}^\circ \]
\[\]
∴ \[\cos^{- 1} \left( \cos {350}^\circ \right) - \sin^{- 1} \left( \sin {350}^\circ \right) = {20}^\circ\]
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