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

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

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

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

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

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

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

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

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