Prove that tan−1(1+cosxsinx),−π<x<π

Prove that tan−1(1+cosxsinx)tan−1(1+cosxsinx)=tan−1(2cos2x/22sinx/2.cosx/2)=tan−1(tanx/2)=2x (∵−π<x<π)(−2π<2x<2π)

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Prove that ^{-1}( { x}{1+ x} ), - < x <

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Prove that
$tan^{- 1} (\frac{sin x}{1 + cos x}), - π < x < π$

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Prove that

tan^{- 1} (\frac{sin x}{1 + cos x}), - π < x < π

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15 mins ago

Prove that

t a n^{- 1} (\frac{s in x}{1 + cos x})

t a n^{- 1} (\frac{s in x}{1 + cos x}) = t a n^{- 1} (\frac{2 s in x /2. cos x /2}{2 co s ^{2} x /2})

= t a n^{- 1} (t an x /2)

= \frac{x}{2}

(∵ - π < x < π)

(- \frac{π}{2} < \frac{x}{2} < \frac{π}{2})

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Question Text	Prove that $tan^{- 1} (\frac{sin x}{1 + cos x}), - π < x < π$
Answer Type	Text solution:1
Upvotes	150