MCQ
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
- ✓$11$
- B$22$
- C$33$
- D$7$
✓
Answer
Correct option: A.
$11$
a
$3 \sin x+4 \cos x=k+1$
$3 \sin x+4 \cos x=k+1$
$\Rightarrow k +1 \in\left[-\sqrt{3^{2}+4^{2}}, \sqrt{3^{2}+4^{2}}\right]$
$\Rightarrow k +1 \in[-5,5]$
$\Rightarrow k \in[-6,4]$
No. of integral values of $k =11$
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