Mathematics - Trigonometric Equation Question with Solution | TestHub

The given equation is $\tan x+\sec x=2\cos x\Rightarrow \sin x+1=2{\cos }^{2}x$ $$\begin{array}{rl}& \Rightarrow \sin x+1=2\left(1-{\sin }^{2}x\right)\Rightarrow 2{\sin }^{2}x+\sin x-1=0\\ & \Rightarrow (2\sin x-1)(\sin x+1)=0\Rightarrow \sin x=\frac{1}{2},-1\Rightarrow x=30^{\circ },150^{\circ },270^{\circ }\end{array}$$