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

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

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

y=1/((1+tan theta)^(sin theta-cos theta)+(cot theta)^(cos theta-cot theta))+ 1/((1+tan theta)^(cos theta-sin theta)+(cot theta)^(sin theta-cottheta)) +1/((1+tan theta)^(cos theta-cot theta)+(cot theta)^(cot theta-sin theta)) then (dy)/(dx) at theta=pi/3 is

y=1/((1+tan theta)^(sin theta-cos theta)+(cot theta)^(cos theta-cot theta))+ 1/((1+tan theta)^(cos theta-sin theta)+(cot theta)^(sin theta-cottheta)) +1/((1+tan theta)^(cos theta-cot theta)+(cot theta)^(cot theta-sin theta)) then (dy)/(dx) at theta=pi/3 is

cos ect theta(sec theta-1)-cot theta(1-cos theta)=tan theta-sin theta

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

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

cos ec theta(sec theta-1)-cot theta(1-cos theta)=tan theta-sin theta

(sin theta)/(1-cot theta)+(cos theta)/(1-tan theta)=(a)theta(b)1(c)cos theta-sin theta(d)cos theta+sin theta

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