A) 0
B) \[-1\]
C) 1
D) 2
Correct Answer: C
Solution :
\[\sin x+{{\sin }^{2}}x=1\] \[\Rightarrow \] \[\sin x=1-{{\sin }^{2}}x\,\,\,\Rightarrow \,\,\,\,\sin x={{\cos }^{2}}x\] Now, \[{{\cos }^{8}}x+2{{\cos }^{6}}x+{{\cos }^{4}}x\] \[={{\sin }^{4}}x+2{{\sin }^{3}}x+{{\sin }^{2}}x\] \[={{({{\sin }^{2}}x+\sin x)}^{2}}=1\]\[[\because \,\,\,\,(\sin x+{{\sin }^{2}}x)=1]\]You need to login to perform this action.
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