A) 1
B) 2
C) 3
D) 0
Correct Answer: A
Solution :
Given \[\sin x+{{\sin }^{2}}x=1\] \[\Rightarrow \] \[\sin x=1-{{\sin }^{2}}x\] \[\Rightarrow \] \[\sin x={{\cos }^{2}}x\] Now, \[{{\cos }^{12}}x+3{{\cos }^{10}}x+3{{\cos }^{8}}x+{{\cos }^{6}}x\] \[={{\sin }^{6}}x+3{{\sin }^{5}}x+3{{\sin }^{4}}x+{{\sin }^{3}}x\] \[=\,{{({{\sin }^{2}}x+\sin x)}^{3}}\] \[={{(1)}^{3}}=1\]You need to login to perform this action.
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