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

Prove that: (sin^(3) theta + cos^(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 that (cot theta -cos theta )/( cot theta +cos theta ) =(cos ec theta -1)/( cosec theta +1)

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

(1+cos 2 theta)/(sin 2 theta)=cot theta

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

If sin theta - cos theta = 3/5, sin theta cos theta = __________

Prove that: sin theta (1 + tan theta) + cos theta (1+ cot theta) = sec theta + cosec theta .

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

Simplify: (sin^(3) theta + cos^(3) theta)/(sin theta + cos theta) + sin theta cos theta