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Evaluate ππsin-1(sin 3π4)+cos-1(cosπ)+tan-1(1). - Mathematics

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Question

Evaluate $\sin^{- 1} (\sin \frac{3 π}{4}) + \cos^{- 1} (\cos π) + \tan^{- 1} (1)$ .

Sum

Solution

$\sin^{- 1} (\sin \frac{3 π}{4}) + \cos^{- 1} (\cos π) + \tan^{- 1} (1)$

= $\sin^{- 1} [\sin (π - \frac{π}{4})] + π + \tan^{- 1} (\tan \frac{π}{4})$

= $\frac{π}{4} + π + \frac{π}{4}$

= $\frac{π}{2} + π$

= $\frac{3 π}{2}$

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Inverse Trigonometric Functions - Inverse Trigonometric Functions - Principal Value Branch

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