A) \[16{{\cos }^{3}}x{{\sin }^{2}}x\]
B) \[16{{\sin }^{3}}x{{\cos }^{2}}x\]
C) \[4{{\cos }^{3}}x{{\sin }^{2}}x\]
D) \[4{{\sin }^{3}}x{{\cos }^{2}}x\]
Correct Answer: A
Solution :
\[2\,\cos x-\cos \,3x-\cos \,5x=2\cos x(1-\cos 4x)\] \[=2\cos x\,2{{\sin }^{2}}2x\]\[=4\,\cos x\,{{\sin }^{2}}\,2x=16\,{{\sin }^{2}}x\,{{\cos }^{3}}x\].
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