Question

The number of solutions of the equation tan x + sec x = 2 cos x and cos x ≠ lying in the interval (0, 2π) is

• A. (A) 2
• B. (B) 1
• C. (C) 0
• D. (D) 3

Answer 1

Answer: (D)

(D) 3

Answer 2

Explanation:
tan⁡x+sec⁡x=2cos⁡x1+sin⁡x=2−2sin2⁡x2sin2⁡x+sin⁡x−1=0(2sin⁡x−1)(sin⁡x+1)=0sin⁡x=−1,12Therefore, number of solutions in (0,2π)=3