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

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

Grade:12

2 Answers

bharat bajaj IIT Delhi
askIITians Faculty 122 Points
7 years ago
tan x + sec x = 2 cos x
sin x + 1 = 2 cos2x
sin x + 1 = 2 (1 - sin2x)
2 sin2x + sin x - 1 = 0
Solve for sin x:
sin x = - 1, or sin x = 1/2
sin x = -1 means cos x = 0, which is not possible as tan x cant be infinity
Therfore, sin x = 1/2
x = p or x = p - (p / 6), in the interval [0, 2p]
x = p or x = 5p / 6 are the two solutions
Thanks
Bharat Bajaj
IIT Delhi
askiitians faculty
Apptica Corporations
37 Points
7 years ago
2 solutions pi/6 5pi/6

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