A) \[cos\text{ }2x\]
B) \[2\,cos\,x\]
C) \[co{{s}^{2}}x\]
D) \[1+\cos x\]
Correct Answer: B
Solution :
The given expression can be written as \[\frac{(\cos 6x+\cos 4x)+5(\cos 4x+\cos 2x)+10(\cos 2x+1)}{\cos 5x+5\cos 3x+10\cos x}\]\[=\frac{2\cos 5x\cos x+5.2\cos 3x\,cos\,x+10.2{{\cos }^{2}}x}{\cos 5x+5cos3x+10cosx}\] \[=\frac{2\cos x(\cos 5x+5\cos 3x+10\cos x)}{\cos 5x+5\cos 3x+10\cos x}=2\cos x\]
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