Mathematics - Trigonometric Equation Question with Solution | TestHub

The given equation can be written as

$\frac{1+\sin x}{\cos x}=2\cos x$

$\Rightarrow 1+\sin x=2{\cos }^{2}x=2\left(1-{\sin }^{2}x\right)$

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

$\Rightarrow (1+\sin x)(2\sin x-1)=0$

$\Rightarrow \sin x=-1$ or $1/2$

Now $\sin x=-1\Rightarrow \tan x$ and $\sec x$ not defined. $\sin x=1/2\Rightarrow x=\pi /6$ or $5\pi /6$.

∴ The required number of solution is 2 .