Question

given that sin theta + 2 cos theta = 1 , then prove that 2 sin theta -cos theta = 2

Answer 1

let theta =@
given ,
sin@+2cos@=1
divide cos@ both side
sin@/cos@ +2cos@/cos@=1/cos@
tan@+2=sec@
now squaring both side
tan^2@+4+4tan@=sec^2@=1+tan^2@

because sec^2x-tan^2x=1

now
4+4tan@=1
tan@=-3/4
if we assume @ lies between (pi/2, pi)
then ,
sin@=3/5
cos@=-4/5

now
LHS=2sin@-cos@
put cos and sin value
=2 (3/5)-(-4/5)=6/5+4/5=10/5=2=RHS

Answer 2

here is your correct answer