Question

Number of solution of equation $4\cos \theta -3\sec \theta =\tan \theta$ in $[0,\pi ]$ is:

• A. $4$
• B. $3$
• C. $0$
• D. $2$

Answer 1

The correct option is A $4$

Given: $4\cos \theta -3\sec \theta =\tan \theta$

$\Rightarrow 4\cos \theta -\frac{3}{\cos \theta }=\frac{\sin \theta }{\cos \theta }$

$\Rightarrow 4{\cos }^2\theta -3=\sin \theta$

$\Rightarrow 4-4{\sin }^2\theta -3=\sin \theta$

$\Rightarrow 4{\sin }^2\theta +\sin \theta -1=0$

$\Rightarrow \sin \theta =\frac{-1\pm \sqrt{1+16}}{8}$

$\Rightarrow \sin \theta =\frac{-1\pm \sqrt{17}}{8}$

$\Rightarrow 4$ solutions