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Write the principal value of\(tan^{-1}(1)+cos^{-1}(-\frac{1}{2})\). |
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Answer» Given tan-1(1) + cos-1 (-1/2) We know that cos-1 (-θ) = π – cos-1 θ \(=\frac{\pi}{4}+[\pi-\frac{\pi}{3}]\) \(=\frac{\pi}{4}+\frac{2\pi}{3}\) \(=\frac{3\pi+8\pi}{12}\) \(=\frac{11\pi}{12}\) \(\therefore tan^{-1}(1)+cos^{-1}(-\frac{1}{2})=\frac{11\pi}{12}\) |
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