Question

The number of solution(s) of the equation $a\sin x+b\cos x=c\text{where}|c|>\sqrt{a^2+b^2}\text{is}:$

• A. Infinite
• B. $2$
• C. $1$
• D. No solution

Answer 1

The correct option is D No solution

We know, range of $a\sin x+b\cos x$ is $[-\sqrt{a^2+b^2},\sqrt{a^2+b^2}]$
Since $c$ is not in the range of $a\sin x+b\cos x$
$\therefore$ There is no solution for this equation