Question

The equation $a\sin x+b\cos x=c$, where $\left|c\right|>\sqrt{a^2+b^2}$ has

• A. A unique solution
• B. Infinite number of solutions
• C. No solution
• D. None of the above

Answer 1

Answer: (C)

No solution

Since, $|a\sin x=b\cos x|\le \sqrt{a^2+b^2},\forall x\in R$
$\Rightarrow \left|c\right|\le \sqrt{a^2+b^2}$
But $\left|c\right|>\sqrt{a^2+b^2}$
$\therefore a\sin x=b\cos x=c$
It does not hold for any $x\in R$
So, it has no solution.