If `cos theta + sin theta =1` prove that `cos theta -sin theta =+-1`

If cos theta + sin theta =1 , prove that cos theta - sin theta = pm 1.

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

If sin theta+cos theta=1 prove that sin theta-cos theta=+-1

If x=(2sin theta)/(1+cos theta+sin theta), then prove that (1-cos theta+sin theta)/(1+sin theta) is equal to x

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

(1 + cos theta + sin theta) / (1 + cos theta-sin theta) = (1 + sin theta) / (cos theta)

cos theta/(1+sin theta)=(1-sin theta)/cos theta

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.