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Q.

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

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a

x = 1 – y

b

x2 = 1 – y

c

x2 = 1 + y

d

y2 = 1 – x

answer is D.

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Detailed Solution

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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