Question

The sum of the real roots of ${\cos }^{6}x+{\sin }^{4}x=1$ in the interval $-\pi <x<\pi$ is equal to

• A. $0$
• B. $\pi$
• C. $-\pi$
• D. $\frac{\pi }{2}$

Answer 1

Answer: (A)

$0$

we note that if $\alpha$ is a root of the given equation then $-\alpha$ is also a root
so the sum has to be zero