Question

If $f\left(x\right)=\sin x-ax$ is decreasing $\forall x\in R,$ then

• A. $a>1$
• B. $a<1$
• C. $a>\frac{1}{2}$
• D. $a<\frac{1}{2}$

Answer 1

The correct option is A $a>1$

Given, $f\left(x\right)=\sin x-ax$
$\Rightarrow f^{\prime }\left(x\right)=\cos x-a$
For decreasing $f^{\prime }\left(x\right)<0$
$\Rightarrow \cos x-a<0$
$\Rightarrow \cos x<a$
$\Rightarrow a>1$