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  • Number of solutions of the equation tan x + sec x = 2 cos x lying in the interval [0, 2π] is A. 0 B. 1 C. 2 D. 3

Number of solutions of the equation \tan x + sec x = 2 \cos x  lying in the interval [0, 2 \pi ] is

A. 0

B. 1

C. 2

D. 3

Answers (1)

The answer is the option (c). 

\\\\ \tan x+\sec x=2\cos x \\\\ \frac{\sin x+1}{\cos x}=2\cos x \\\\ 1+\sin x - 2\cos ^{2}x=0 \\\\ 1+\sin x - 2+2\sin ^{2}x=0 \\\\ 2\sin ^{2}x+\sin x - 1=0 \\\\

Since the equation is a quadratic equation in \sin x. So, there will be two solutions.

Hence, correct option is (c).   

Posted by

infoexpert21

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