Trigonometry

The number of solution of tan x + sec x = 2 cos x in [0, 2π) is

  1. 0
  2. 1
  3. 2
  4. 3

Answer

tan x + sec x = 2 cos x

Multiply equation by cos x

1 + sin x = 2 cos2 x

1 + sin x = 2(1 - sin2 x)

2 sin2 x + sin x - 1 = 0

(2 sin x - 1)(1 + sin x) = 0

sin x = 1/2 ; sin x = -1

So, there can be three solutions: 30°, 150° and 270°.

The correct option is D.