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Inverse Trigonometric Functions
Inverse Trigonometric Functions
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Question

cos⁡−1(cos⁡(−5))+sin⁡−1(sin⁡(6))−tan⁡−1(tan⁡(12)){\cos ^{ - 1}}(\cos ( - 5)) + {\sin ^{ - 1}}(\sin (6)) - {\tan ^{ - 1}}(\tan (12)) is equal to : (The inverse trigonometric functions take the principal values)

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Solution

cos⁡−1(cos⁡(−5))+sin⁡−1(sin⁡(6))−tan⁡−1(tan⁡(12)){\cos ^{ - 1}}(\cos ( - 5)) + {\sin ^{ - 1}}(\sin (6)) - {\tan ^{ - 1}}(\tan (12)) =(2π−5)+(6−2π)−(12−4π) = (2\pi - 5) + (6 - 2\pi ) - (12 - 4\pi ) =4π−11 = 4\pi - 11.

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