Question

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

Options

• 2

• 3

• 0

• 1

Answer 1

The number of solution of tan x + sec x = 2 cos x in [0, 2π] is 3.

Explanation:

tan x + sec x = 2 cos x

⇒ 1 + sin x = 2 cos²x

⇒ 1 + sin x = 2(1 − sin²x)

⇒ 2 sin²x + sin x − 1 = 0

⇒ (2 sin x − 1)(1 + sin x) = 0

⇒ sin x = `1/2`, sin x = −1

So there are three solutions like x = 30°, 150°, 270°