Question

The expression $\frac{\cos 6x+6\cos 4x+15\cos 2x+10}{\cos 5x+5\cos 3x+10\cos x}$ is equal to

• A. $\cos 2x$
• B. $2\cos x$
• C. ${\cos }^{2}x$
• D. $1+\cos x$

Answer 1

The correct option is B $2\cos x$

$\frac{\cos 6x+6\cos 4x+15\cos 2x+10}{\cos 5x+5\cos 3x+10\cos x}=\frac{(\cos 6x+\cos 4x)+5(\cos 4x+\cos 2x)+10(\cos 2x+1)}{\cos 5x+5\cos 3x+10\cos x}=\frac{2\cos 5x\cos x+5\left(2\cos 3x\cos x\right)+10\left(2{\cos }^{2}x\right)}{\cos 5x+5\cos 3x+10\cos x}=\frac{2\cos x(\cos 5x+5\cos 3x+10\cos x)}{\cos 5x+5\cos 3x+10\cos x}=2\cos x$