The number of integral values of
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 $\mathrm{k}=11$