A) \[2\cos x\]
B) \[\cos x\]
C) \[2sinx\]
D) \[sinx\]
Correct Answer: A
Solution :
Numerator of given expression \[=(\sin 8x+\sin 6x)+6(\sin 6x+\sin 4x)\]\[+12(\sin 4x+\sin 2x)\] \[=2\sin 7x\cos x+12\sin 5x\cos x+24\sin 3x\cos x\] \[=2\cos x(\sin 7x+6\sin 5x+12\sin 3x)\] Hence, given expression \[=\frac{2\cos x(\sin 7x+6\sin 5x+12sin3x)}{(\sin 7x+6\sin 5x+12\sin 3x)}=2\cos x\]
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