Question

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

Answer 1

\[\sin \theta+2 \cos \theta=1 \]

\[\sin \theta=1-2 \cos \theta\]

Square both sides and use identity

\[\sin^2 \theta = 1 + 4\cos^2 \theta - 4\cos \theta\]
\[1 - \cos^2 \theta =1+4\cos^2θ−4\cosθ\]

\[4\cos \theta = 5 \cos^2 \theta\]

\[\cos \theta = 4/5\]

Now try to calculate!

Answer 2

Do not do the last 2 steps like that.
Take cos theta as x
and then find out the solution of the quadratic equation
5x^2 - 4x = 0

Understood? :)