Question

given that sin theta + 2 cos theta is equal to 1 then prove that 2 sin theta minus cos theta is equal to 2​

Answer 1

given that:

sinx+2cosx=1

(where theta is x)

by squaring to both sides...

(sinx+2cosx)^2=1^2

sin^2x+4cos^2x+4sinxcosx=1

(.:,sin^2x+cos^2x=1)

then,

(1-cos^2x)+4(1-sin^2x)+4sinxcosx=1

1-cos^2x+4-4sin^2x+4sinxcosx=1

-(2sinx-cosx)^2+1+4=1

-(2sinx-cosx)^2+5=1

-(2sinx-cosx)^2=-4

on under roots of both sides

2sinx-cosx=2

Hence proved...