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Question

Find the general solution of the following questions
cosx=2x
sin2x+cosx=0.

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Solution

sin2x+cosx=0
sin2x=2sinxcosx
2sinxcosx+cosx=0
cosx(2sinx+1)=0

cosx=0 2sinx=1
sinx=1/2
General solution for cosx=0
x=(2n+1)π/2,nz
x=2nπ±π/2,nz
General solution for sinx=1/2
let sinx=siny(1)
sinx=1/2(2)
From (1) & (2)
siny=1/2
siny=sin7π6
y=7π6
General solution =x=nπ+(1)ny,nz
put y=7π6
x=nπ+(1)n7π6,nz
Hence for cosx=0,x=(2n+1)π/2,nz
for sinx=1/2,x=nπ+(1)n7π6,nz

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