" 18.Given that "sin theta+2cos theta=1" ,then prove that "2sin theta-cos theta=-2

If sin theta+ sin^2 theta = 1 , prove that cos^2 theta+ cos^4 theta = 1 .

If sin theta+ sin^(2)theta=1 , then prove that cos^(2) theta+cos^(4) 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

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=pm sqrt(2) sin theta .

If sin theta+sin^(2)theta=1, prove that cos^(2)theta+cos^(4)theta=1

Prove that sin^(4) theta + cos^(4) theta = 1 - 2 sin^2 theta cos^(2) theta

Prove that (sin theta+cos theta)/(sin theta- cos theta) + (sin theta - cos theta)/(sin theta + cos theta) = ( 2sec^(2) theta)/(tan^(2) theta -1) .

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