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Number of solutions of the equation tan x + sec x = 2 cos x, lying in the interval [0, 2p] is
tan x + sec x = 2 cos xsin x + 1 = 2 cos2xsin x + 1 = 2 (1 - sin2x)2 sin2x + sin x - 1 = 0Solve for sin x:sin x = - 1, or sin x = 1/2sin x = -1 means cos x = 0, which is not possible as tan x cant be infinityTherfore, sin x = 1/2x = p or x = p - (p / 6), in the interval [0, 2p]x = p or x = 5p / 6 are the two solutionsThanksBharat BajajIIT Delhiaskiitians faculty
2 solutions pi/6 5pi/6
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