^2 A (3 - 4 ^2 A)^2 + ^2 A (3 - 4 ^2 A)^2 = - Vidyadip

MCQ

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

A
$\cos 4A$
B
$sin 4 A$
✓
$1$
D
None of these

✓

Answer

Correct option: C.

$1$

c
(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 $1.$

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