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Question
Number of solutions of the equation tan x + sec x = 2 cosx lying in the interval [0, 2π] is ______.
Options
0
1
2
3
Solution
Number of solutions of the equation tan x + sec x = 2 cosx lying in the interval [0, 2π] is 3.
Explanation:
tanx + sec = 2cosx
sin + 1 = cos2x = sinx + 1= 2 - sin2x
2sin2x + sinx -1 = 0
(2sinx - 1) (sin + 1) = 0
but sinx = -1
`x= (3pi)/2`
`sinx = 1/2 = sin(pi/6)`
therefore the general solution is,
`x = npi + (-1)^n.pi/6`
`x = ...pi/6, (5pi)/6`
therefore, the number of solutions in the given interval is 3.
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