{cos ^2}A{(3 - 4{cos ^2}A)^2} + {sin ^2}A{(3 | vedclass

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

Question

(c) ${\cos ^2}A{(3 - 4{\cos ^2}A)^2} + {\sin ^2}A{(3 - 4{\sin ^2}A)^2}$ 

$ = {(3\cos A - 4{\cos ^3}A)^2} + {(3\sin A - 4{\sin ^3}A)^2}$

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(c) ${\cos ^2}A{(3 - 4{\cos ^2}A)^2} + {\sin ^2}A{(3 - 4{\sin ^2}A)^2}$ 

$ = {(3\cos A - 4{\cos ^3}A)^2} + {(3\sin A - 4{\sin ^3}A)^2}$ 

$ = {(\cos 3A)^2} + {(\sin 3A)^2} = 1$. 

Trick : Put $A = \frac{\pi }{2},{0^o}$, the value of expression remains $1$,

therefore it is independent of $A$ and is equal to $1.$

${\cos ^2}A{(3 - 4{\cos ^2}A)^2} + {\sin ^2}A{(3 - 4{\sin ^2}A)^2} = $

Similar Questions

$cosec^2\theta $ = $\frac{4xy}{(x +y)^2}$ is true if and only if

If $\sin 2\theta + \sin 2\phi = 1/2$ and $\cos 2\theta + \cos 2\phi = 3/2$, then ${\cos ^2}(\theta - \phi ) = $

Prove that $\cos ^{2} 2 x-\cos ^{2} 6 x=\sin 4 x \sin 8 x$

$\sqrt 3 \,{\rm{cosec}}\,{20^o} - \sec \,{20^o} = $

The exact value of $cos^273^o + cos^247^o + (cos73^o . cos47^o )$ is