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If cot^{-1}({ a})- tan^{-1}({ a})=x, then x is

Question

If $co t^{- 1} (cos a) - t a n^{- 1} (cos a) = x$ , then $sin x$ is

t a n^{2} \frac{α}{2}

co t^{2} \frac{α}{2}

tan α

co t \frac{α}{2}

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Benjamin Discussed

co t^{- 1} (cos a) - t a n^{- 1} (cos a) = x

, then

sin x

10 mins ago

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10 mins ago

Text solutionVerified

co t^{- 1} (cos a) - t a n^{- 1} (cos a) = x

t a n^{- 1} (\frac{1}{cos a}) - t a n^{- 1} (cos a) = x

t a n^{- 1} \frac{\frac{1}{cos a} - cos a}{1 + \frac{1}{cos a} cos a} = x

t a n^{- 1} \frac{1 - cos a}{2 cos a} = x

\frac{1 - cos a}{2 cos a} = tan x

\frac{2 cos a}{1 - cos a} = cot x

sin x = \frac{1 - cos a}{1 + cos a} = \frac{2 sin ^{2} \frac{α}{2}}{2 cos ^{2} \frac{α}{2}}

t a n^{2} \frac{α}{2}

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Question Text	If $co t^{- 1} (cos a) - t a n^{- 1} (cos a) = x$ , then $sin x$ is
Answer Type	Text solution:1
Upvotes	150