Find the general solution for each of the following equations: sin 2x + cos x = 0

Solution:

The given equation is,

sin 2x + cos x = 0

2sin x cos x + cos x = 0 [By double angle formulas, sin 2A = 2sin A cos A]

cos x(2sin x + 1) = 0

cos x = 0 or 2sin x + 1 = 0

cos x= 0 or sin x = -1/2

We know that cos x = 0 when x = π/2 and sin x = -1/2 when x = 7π/6. Thus,

cos x = cos π/2 or sin x = sin 7π/6, where n∈Z.

x = [(2n + 1)π/2] or x = [nπ + (-1)ⁿ7π/6], where n∈Z.

NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.4 Question 7

Find the general solution for each of the following equations: sin 2x + cos x = 0

Summary:

The general solutions of sin 2x + cos x = 0 are x = [(2n + 1)π/2] or [nπ + (-1)ⁿ7π/6], where n∈Z.