" HOTS If "sin theta+2cos theta=1," prove that "2sin theta-cos theta=2

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

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

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

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