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3.Trigonometrical Ratios, Functions and Identities
easy
${\cos ^2}A{(3 - 4{\cos ^2}A)^2} + {\sin ^2}A{(3 - 4{\sin ^2}A)^2} = $
A
$\cos 4A$
B
$sin 4 A$
C
$1$
D
એકપણ નહિ.
Solution
(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 $1.$
Standard 11
Mathematics
