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Question

Find the general solution of the equation sin2x+cosx=0

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Solution

Step 1: Simplification
Given : sin2x+cosx=0
2sinxcosx+cosx=0
cosx=0 or 2sinx+1=0
cosx=0 or sinx=12

Step 2: General solution for cosx=0
The general solution is x=(2n+1)π2 where nZ

Step 3: General solution for sinx=12
sinx=12
sinx=sin7π6
x=nπ+(1)n7π6, where nZ

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