Q. 534.0( 7 Votes )

# 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

Answer :

We have, tan x + sec x = 2 cos x

⇒ 1+sin x = 2cos^{2}x

⇒ 2cos^{2}x-sin x-1 = 0

⇒ 2(1-sin^{2}x)-sin x-1 = 0

⇒ 2-2sin^{2}x-sin x-1 = 0

⇒ 2sin^{2}x+sin x-1 = 0

Since, the equation is a quadratic equation in sin x, it will have 2 solutions.

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