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3.Trigonometrical Ratios, Functions and Identities
medium
यदि $\sin x + {\sin ^2}x = 1,$ तब ${\cos ^8}x + 2{\cos ^6}x + {\cos ^4}x = $
A
$0$
B
$-1$
C
$2$
D
$1$
Solution
(d) We have $\sin x + {\sin ^2}x = 1\,\,$
$\Rightarrow \,\,\sin x = {\cos ^2}x$
$\therefore$ ${\cos ^8}x + 2{\cos ^6}x + {\cos ^4}x $
$= {\sin ^4}x + 2{\sin ^3}x + {\sin ^2}x$
$ = {(\sin x + {\sin ^2}x)^2} = 1$.
Standard 11
Mathematics
