Question

The number of solutions of the equation sin 2x – 2 cosx + 4 sinx = 4 in the interval [0, 5π] is ______.

Options

• 3

• 5

• 4

• 6

Answer 1

The number of solutions of the equation sin 2x – 2 cosx + 4 sinx = 4 in the interval [0, 5π] is 3.

Explanation:

sin2x – 2cosx + 4sinx = 4

⇒ 2sinx.cosx – 2cosx + 4sinx – 4 = 0

⇒ (sin x – 1)(cos x – 2) = 0

∵ cosx – 2 ≠ 0

∴ sinx = 1

∴ x = `π/2, (5π)/2, (9π)/2`