Question

If $f\left(x\right)=\frac{\sin x+b\cos x}{\sin x+4\cos x}$ is monotonic increasing, then-

• A. $b<8$
• B. $b<4$
• C. $b>4$
• D. $b>8$

Answer 1

Answer: (B)

$b<4$

We know that
$f\left(x\right)=\frac{a\sin x+b\cos x}{c\sin x+d\cos x}$
It will be monotonic increasing when $ad-bc>0$

Given $f\left(x\right)=\frac{\sin x+b\cos x}{\sin x+4\cos x}$ is monotonic increasing
So, $4-b>0$
$\Rightarrow b<4$