The number of integer triplets $(a,b,c)$ such that $a+b\cos(2x)+c\sin^2x=0$ for all $x$

Question

The number of integer triplets $(a,b,c)$ such that $$a+b\cos(2x)+c\sin^2x=0\quad\text{for all $x$}$$ is

• (A) $0$
• (B) $1$
• (C) $3$
• (D) infinitely many

I tried to break $\cos 2x$ and write it in sine form, but got confused.

Answer 1

Hint: $\cos{2x} = 1-2\sin^2{x}$.