Write tan−1(1−cosx1+cosx) in its simplest form.

tan−1(1−cos x 1+cos x )=tan−1⎝⎛2sin22x 2cos22x ⎠⎞=tan−1⎝⎛2sin22x2cos22x ⎠⎞=tan−1(cot22x )=tan−1(cot2x )=tan−1(tan(2π −2x ) )=2π −2x

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Write ^{-1} ( {{1+ x}}{{1- x}} ) in its simplest form.

Question

Write $tan^{- 1} (\frac{1 + cos x}{1 - cos x})$ in its simplest form.

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Charlotte Discussed

Write

tan^{- 1} (\frac{1 + cos x}{1 - cos x})

in its simplest form.

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9 mins ago

tan^{- 1} (\frac{1 + cos x}{1 - cos x}) = tan^{- 1} ⎝ ⎛ \frac{2 cos ^{2} \frac{x}{2}}{2 sin ^{2} \frac{x}{2}} ⎠ ⎞ = tan^{- 1} ⎝ ⎛ \frac{2 cos ^{2} \frac{x}{2}}{2 sin ^{2} \frac{x}{2}} ⎠ ⎞ = tan^{- 1} (cot^{2} \frac{x}{2}) = tan^{- 1} (cot \frac{x}{2}) = tan^{- 1} (tan (\frac{π}{2} - \frac{x}{2})) = \frac{π}{2} - \frac{x}{2}

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Question Text	Write $tan^{- 1} (\frac{1 + cos x}{1 - cos x})$ in its simplest form.
Answer Type	Text solution:1
Upvotes	150