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

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

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

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

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

Prove the following identity : (sin theta)/(1+cos theta)+ (sin theta)/(1-cos theta)= 2/(sin theta) .

Prove each of the following identities : (i) (sin theta - cos theta)/(sin theta + cos theta) + ( sin theta+ cos theta)/(sin theta - cos theta) = (2)/((2 sin^(2) theta -1)) (ii) (sin theta + cos theta ) /(sin theta - cos theta) + ( sin theta - cos theta) /(sin theta + cos theta) = (2) /((1- 2 cos^(2) theta))

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

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

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