sin theta+2cos theta=1" prove that "2sin theta-cos theta=2

Given that sin theta+2cos theta=1 then prove that 2sin theta-cos theta=2

If cos theta+sin theta=sqrt(2)cos theta prove that cos theta-sin theta=sqrt(2)sin theta

If cos theta+sin theta=sqrt(2)cos theta, prove that cos theta-sin theta=sqrt(2)sin theta

If cos theta + sin theta =sqrt(2) cos theta prove that cos theta -sin theta =sqrt(2) sin theta

Prove that : (1-sin theta cos theta)/ (cos theta (sec theta - cosec theta)) times (sin^2 theta - cos^2 theta)/(sin^3 theta + cos^3 theta) = sin theta

If costheta + sin theta = sqrt2 cos theta , prove that cos theta - sin theta = sqrt2 sin theta .

Prove: (cos^2theta)/(1-tan theta) + (sin^3 theta)/(sin theta - cos theta ) = 1 + sin theta cos theta

Evaluate the following determinants: (b) |(cos theta, -sin theta),(sin theta, cos theta)| = cos theta (cos theta) - sin theta(-sin theta) = cos^(2) theta + sin^(2) theta = 1

If cos theta+sin theta=sqrt(2)cos theta then prove that cos theta-sin theta=sqrt(2)sin theta

If cos theta+sin theta=sqrt 2 cos theta ,then prove that cos theta-sin theta = sqrt 2 sin theta .