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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
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.
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