Question:
The number of integral values of ' $k$ ' for which the equation $3 \sin x+4 \cos x=k+1$ has a solution, $k$ $\in R$ is
Solution:
$3 \sin x+4 \cos x=k+1$
$\Rightarrow \mathrm{k}+1 \in\left[-\sqrt{3^{2}+4^{2}}, \sqrt{3^{2}+4^{2}}\right]$
$\Rightarrow \mathrm{k}+1 \in[-5,5]$
$\Rightarrow \mathrm{k} \in[-6,4]$
No. of integral values of $\mathrm{k}=11$