Trigonometric Identities Question 254
Question: The number of solution of $ \tan x+\sec x=2\cos x $ in $ (0,2\pi ) $ is
Options:
A) 2
B) 3
C) 0
D) 1
Show Answer
Answer:
Correct Answer: B
Solution:
The given equation is $ \tan x+\sec x=2\cos x; $
$ \Rightarrow \sin x+1=2{{\cos }^{2}}x\Rightarrow \sin x+1=2(1-{{\sin }^{2}}x); $
$ \Rightarrow ,2{{\sin }^{2}}x+\sin x-1=0; $
$ \Rightarrow ,(2\sin x-1)(sinx+1)=0\Rightarrow sin,x=\frac{1}{2},-1.; $
$ \Rightarrow x=30{}^\circ ,150{}^\circ ,270{}^\circ . $
BETA
