Question

If $e^{({\sin }^{2}x+{\sin }^{4}x+{\sin }^{6}x+...\infty ){\log }_{e}2}$ satisfies the equation $x^2+7x+16=0$ then the value of $\frac{2\cos x}{\sin x+2\cos x}(0<x<\frac{\pi }{2})$ is

• A. $\frac{1}{2}$
• B. $\frac{3}{2}$
• C. $\frac{5}{1}$
• D. No real solution of $x$ is possible

Answer 1

The correct option is D No real solution of $x$ is possible

Given equation:

$x^2+7x+16=0$

$\therefore x=\frac{-7\pm \sqrt{7^2-4\times 1\times 16}}{2\times 1}=\frac{-7\pm \sqrt{-15}}{2}$

The quadratic equation doesn't have real roots and so the value of $\sin x$ or $\cos x$ if solved from that equation cannot be real.