किसी theta inleft(frac{pi}{4}, frac{pi}{2}rig | vedclass

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Question

$3\,{(1 - \sin 2	heta )^2}\, + \,6(1 + \sin 2	heta )\, + \,4\,{\sin ^6}	heta $

$ = 3\,(1 - 2\sin \,2	heta  + {\sin ^2}2	heta ) + \,6 + 6\

Vedclass · Accepted Answer

$13 - 4\,{\cos ^6}\,	heta \,$

Vedclass · Answer

$3\,{(1 - \sin 2	heta )^2}\, + \,6(1 + \sin 2	heta )\, + \,4\,{\sin ^6}	heta $

$ = 3\,(1 - 2\sin \,2	heta  + {\sin ^2}2	heta ) + \,6 + 6\sin 2	heta  + \,4\,{\sin ^6}	heta $

$ = \,9 + 3{\sin ^2}2	heta  + 4\,{\sin ^6}	heta $

$ = \,9 + 12{\sin ^2}	heta {\cos ^2}	heta  + 4\,{(1 - {\cos ^2}	heta )^3}$

$ = \,9 + 12(1 - {\cos ^2}	heta ){\cos ^2}	heta  + 4\,(1 - 3{\cos ^2}	heta  + 3{\cos ^4}	heta  - {\cos ^6}	heta )$

$ = \,13 + 12{\cos ^2}	heta  - 12{\cos ^4}	heta  - 12{\cos ^2}	heta  + 12{\cos ^4}	heta  - 4{\cos ^6}	heta $

$ = \,13 - 4{\cos ^6}	heta $

किसी $\theta \in\left(\frac{\pi}{4}, \frac{\pi}{2}\right)$ के लिये, व्यंजक $3(\sin \theta-\cos \theta)^{4}+6(\sin \theta+\cos \theta)^{2}+4 \sin ^{6} \theta$ होगा

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