If $$x=$$$$sin$$⁡$$2tan$$−$$1$$⁡$$2$$, $$y=$$$$sin$$⁡$$12tan$$−$$1$$⁡$$43$$, then

Correct option is 4y2 = 1 – x

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If $x = \sin (2 \tan^{- 1} 2)$ , $y = \sin (\frac{1}{2} \tan^{- 1} \frac{4}{3})$ , then

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x = 1 – y

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detailed solution

Correct option is D

x = sin2θ, where tanθ = 2⇒x=2tan⁡θ1+tan2⁡θ=41+4=45If α=tan−1⁡43,y=sin⁡α2=121−cos⁡α=121−35=15∴y2=15⇒y2=1−x

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If x=sin⁡2tan−1⁡2, y=sin⁡12tan−1⁡43, then

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If $x = \sin (2 \tan^{- 1} 2)$ , $y = \sin (\frac{1}{2} \tan^{- 1} \frac{4}{3})$ , then