Answer :

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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