Question

$f\left(x\right)=\frac{a\sin x+b\cos x}{a\cos x-b\sin x}(\tan x\ne \frac{a}{b})$ is

• A. increasing in domain $f$
• B. Decreasing in domain $f$
• C. Constant
• D. Nothing can be determined

Answer 1

The correct option is A increasing in domain $f$

$f^{\prime }\left(x\right)=\frac{(acosx-bsinx{)}^2+(asinx+bcosx{)}^2}{(acosx-bsinx{)}^2}$
$=\frac{a^2+b^2}{(acosx-bsinx{)}^2}$
$f^{\prime }\left(x\right)=\frac{a^2+b^2}{(acosx-bsinx{)}^2}$