`(costheta - sin theta + 1)/(cos theta + sin theta - 1) `

The value of (sin^3 theta + cos^3 theta)/(sin theta+ costheta)+((cos^3 theta - sin^3 theta))/(cos theta - sin theta) is

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))

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 that (cos theta-sin theta+1)/(cos theta+sin theta-1)=csc theta+cot theta

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

(tan A) / (1-cot A) + (cot A) / (1-tan A) = 1 + tan A + cot A = 1 + sec A cos ecA (1 + cos theta + sin theta) / (1 + cos theta-sin theta) = (1 + sin theta) / (cos theta)

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

What is ( sin theta - cos theta + 1 )/( sin theta + cos theta -1) - ( sin theta + 1 )/( cos theta ) equal to ?