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Question

Find the general solution for the following equation:
sin 2x + cos x = 0


Solution

sin 2x + cos x = 0

2 sin x cos x + cos x = 0

cos x (2 sin x + 1) = 0

Either cos x = 0 or 2sin  x + 1 = 0

x = (2n + 1) π2

or sin x = -12 = - sin π6 = sin (π6), n ϵ Z

x = (2n+1) π2 or x = nπ+(1)n(π6)

x = (2n+1) π2 or x = nπ+(1)n+1(π6)

or x = nπ+(1)n7π6

[sin(π+π6)=sinπ6]

x = (2n+1) π2 or x = nπ+(1)n7π6, n ϵ Z

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