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

Prove that : (tan theta)/(1 -cot theta) + (cot theta)/(1- tan theta) = 1 + cos theta cosec theta

Prove that: (sin2 theta)/(1-cos2 theta)=cot theta

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

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

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

Prove that (1)/(2){(sin theta)/(1+cos theta)+(1+cos theta)/(sin theta)}=(1)/(sin theta)

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

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

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

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