જો x + y = 3 - cos4theta અને x - y = 4 ,sin2t | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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

જો $x + y = 3 - cos4\theta$ અને $x - y = 4 \,sin2\theta$ હોય તો

Similar Questions

જો $x\, sin \theta = y\, sin \, \left( {\theta \,\, + \,\,\frac{{2\,\pi }}{3}} \right) = z\, sin \, \left( {\theta \,\, + \,\,\frac{{4\,\pi }}{3}} \right)$ હોય તો

ત્રિકોણ $ABC$ માટે , $\sin 2A + \sin 2B + \sin 2C = . . ..$

${\sin ^2}\frac{\pi }{8} + {\sin ^2}\frac{{3\pi }}{8} + {\sin ^2}\frac{{5\pi }}{8} + {\sin ^2}\frac{{7\pi }}{8}$ =

સાબિત કરો કે, $\tan 3 x \tan 2 x \tan x=\tan 3 x-\tan 2 x-\tan x$

જો $90^\circ < A < 180^\circ $ અને $\sin A = \frac{4}{5},$ તો $\tan \frac{A}{2} = . . .$