Question

The number of solution of $2cosx-|sinx|,0\le x\le 4\pi$ is

• A. $0$
• B. $2$
• C. $4$
• D. Infinite

Answer 1

The correct option is A $0$

$2\cos x-|\sin x|,0\le x\le 4x$.

In $0\le x\le 4x$

$|\sin x|=\sin x$ when $\sin x>0$

$=-\sin x$ when $\sin x<0$

Let $f\left(x\right)=2\cos x-\sin x,sinx>0$

$=2\cos x+\sin x,\sin x<0$

Now $f\left(x\right)=0\Rightarrow 2\cos x-\sin x=0$

$\Rightarrow \tan x=2$

Not possible for $0\le x\le 4x$

and $2\cos x+\sin x=0$

$\Rightarrow \tan x-2$

Not possible for $0\le x\le 4x$

$\therefore 2\cos x-|\sin x|$ has no sol in $0\le x\le 4x$

Hence, number of sol $=0$