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Question Number 109715 by bobhans last updated on 25/Aug/20

$$\{\begin{array}{l}\sin 2x+\sin 2y=\frac{5}{4}\\ \cos (x-y)=2\sin (x+y)\end{array}where0<x,y<\frac{\pi }{2}$$ $$\cos {}^2(x+y)=?$$ $$△\frac{\mathrm{♭}o\mathrm{♭}}{hans}▽$$

Answered by nimnim last updated on 25/Aug/20

$$\Rightarrow 2\sin (x+y)\cos (x-y)=\frac{5}{4}$$ $$\Rightarrow 2\sin (x+y)2\sin (x+y)=\frac{5}{4}$$ $$\Rightarrow {\sin }^2(x+y)=\frac{5}{16}$$ $$\Rightarrow 1-{\cos }^2(x+y)=\frac{5}{16}$$ $$\Rightarrow {\cos }^2(x+y)=\frac{11}{16}★$$ $$\mathrm{Am}\mathrm{I}\mathrm{right}\mathrm{Sir}??$$

Commented bybobhans last updated on 25/Aug/20

$$good....santuyy$$

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