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Write the value of \(sin^{-1}(\frac{1}{3})-cos^{-1}(-\frac{1}{3})\) |
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Answer» Given sin-1 (1/3) – cos-1 (-1/3) We know that cos-1 (-θ) = π – cos-1 θ \(=sin^{-1}(\frac{1}{3})-[\pi-cos^{-1}(\frac{1}{3})]\) \(=sin^{-1}(\frac{1}{3})-\pi+cos^{-1}(\frac{1}{3})\) \(=sin^{-1}(\frac{1}{3})+cos^{-1}(\frac{1}{3})-\pi\) \(=\frac{\pi}{2}-\pi\) \(=-\frac{\pi}{2}\) \(\therefore sin^{-1}(\frac{1}{3})-cos^{-1}(\frac{1}{3})\)\(=-\frac{\pi}{2}\) |
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