Find the value of the following : tan−1x=21 cos−1x

put xtanθ⇒ θ tan−1xRHS21 cos−1x(1+x1−x)==21cos−1[1+tan2θ1−tan2θ]=21cos−1[cos2θ]=21× 2θ =θtan−1x=LHS

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Find the value of the following : ^{-1} {x} = {1}{2} ^{-1}

Question

Find the value of the following :

$tan^{- 1} x = \frac{1}{2} cos^{- 1} x$

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Luna Discussed

Find the value of the following :

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

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15 mins ago

put

x tan θ \Rightarrow θ tan^{- 1} x

R H S \frac{1}{2} cos^{- 1} x

(\frac{1 - x}{1 + x}) == \frac{1}{2} cos^{- 1}

[\frac{1 - tan ^{2} θ}{1 + tan ^{2} θ}]

= \frac{1}{2} cos^{- 1} [cos 2 θ] = \frac{1}{2} \times 2 θ = θ

tan^{- 1} x = L H S

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Question Text	Find the value of the following : $tan^{- 1} x = \frac{1}{2} cos^{- 1} x$
Answer Type	Text solution:1
Upvotes	150