For any theta , in ,left( {frac{pi }{4}, | vedclass

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

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 $

For any $\theta \, \in \,\left( {\frac{\pi }{4},\frac{\pi }{2}} \right)$, the expression $3\,{\left( {\sin \,\theta - \cos \,\theta } \right)^4} + 6{\left( {\sin \,\theta + \cos \,\theta } \right)^2} + 4\,{\sin ^6}\,\theta $ equals

Similar Questions

The value of $cot\, x + cot\, (60^o + x) + cot\, (120^o + x)$ is equal to :

If $\sin A = n\sin B,$ then $\frac{{n - 1}}{{n + 1}}\tan \,\frac{{A + B}}{2} = $

If $\sin \theta + \sin 2\theta + \sin 3\theta = \sin \alpha $and $\cos \theta + \cos 2\theta + \cos 3\theta = \cos \alpha $, then $\theta$ is equal to

If $\cos \,(\theta - \alpha ) = a,\,\,\sin \,(\theta - \beta ) = b,\,\,$then ${\cos ^2}(\alpha - \beta ) + 2ab\,\sin \,(\alpha - \beta )$ is equal to

$4 \,\,sin5^o \,\,sin55^o \,\,sin65^o$ has the values equal to