Find the number of solution of ` tan x + sec x =2 cos x ` in `[0,2pi]`

Options

A. 2
B. 3
C. 0
D. 1

Answer

A

Explanation

Clearly, given equation is defined for `x ne pi//2, 3pi//2`.
Now,
`"tan" x + "sec" x = 2 "cos" x`
`rArr 1 + "sin" x = 2"cos"^(2) x`
`rArr 2"sin"^(2) x + "sin" x -1 = 0`
`rArr (2"sin" x - 1)("sin" x + 1) = 0`
`rArr "sin" x = (1)/(2), "sin" x = -1`
`rArr x = (pi)/(6), (5pi)/(6), (3pi)/(6), rArr x = (pi)/(6), (5pi)/(6) " " [because x ne (3pi)/(2)]`