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 n∈Z
Step 3: General solution for sinx=−12
sinx=−12
⇒sinx=sin7π6
x=nπ+(−1)n7π6, where n∈Z