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