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

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

1+sin x = 2cos2x

2cos2x-sin x-1 = 0

2(1-sin2x)-sin x-1 = 0

2-2sin2x-sin x-1 = 0

2sin2x+sin x-1 = 0

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

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