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. $2cos\, x$
• C. $cos^2x$
• D. $1 + cos\, x$.

Answer 1

Answer: (B)

The given expression can be written as
$\frac{\left(cos\,6x+cos\,4x\right) + 5\left(cos\,4x + cos\,2x\right)+10\left(cos\,2x+1\right)}{cos\,5x + 5\,cos\,3x +10\,cos\,x}$
$= \frac{2 \,cos \,5x\, cos \,x + 5.2 \,cos\, 3x\, cos\, x + 10.2 cos^{2} \,x}{cos\,5x + 5\,cos\,3x +10\,cos\,x}$
$= \frac{2 \,cos \,x\left(cos \,5x+5\,cos \,3x + 10\,cos \,x\right)}{cos\,5x + 5\,cos\,3x +10\,cos\,x} = 2\,cos\,x$