If x + y = 3 - cos4theta and x - y = 4 ,sin2t | vedclass

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Question

On adding and subtracting

$x = \frac{{3 - \cos 4	heta \, + 4\sin 2	heta }}{2}\,$; $y = \frac{{3 - \cos 4	heta \, - 4\sin 2	heta }}{2}\,$

$x

Vedclass · Accepted Answer

$\sqrt x \, + \,\sqrt y \, = \,2$

Vedclass · Answer

On adding and subtracting

$x = \frac{{3 - \cos 4	heta \, + 4\sin 2	heta }}{2}\,$; $y = \frac{{3 - \cos 4	heta \, - 4\sin 2	heta }}{2}\,$

$x =\frac{{4(1 + \sin 2	heta )\, - \,(1 + \cos 4	heta )}}{2}\,$ ; $y =\frac{{4(1 - \sin 2	heta )\, - \,(1 + \cos 4	heta )}}{2}\,$

$x = 2 (1 + sin2	heta ) - cos^22	heta$ ; $y = 2 (1 - sin2	heta ) - cos^22	heta$

$x = 1 + 2\, sin2	heta + sin^22	heta$ ;$ y = 1 - 2 sin2	heta + sin^22	heta$

$x = (1 + sin2	heta )^2$ ;$y = (1 - sin2	heta )^2$ $\Rightarrow \sqrt x \, + \,\sqrt y \, = \,2$

Alternate : Or put $	heta$ = $\frac{\pi }{4}\,$ and verify

If $x + y = 3 - cos4\theta$ and $x - y = 4 \,sin2\theta$ then

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