Prove that, `(cosec theta-cot theta)^(2)=(1-cos theta)/(1+cos theta)`

(b) cosec theta=1+cot theta

(b) cosec theta=1+cot theta

prove that (cosec theta + cot theta)/(cosec theta- cot theta) = (cosec theta +cot theta)^2

Prove that : (sin theta + sec theta) ^(2) + (cos theta + cosec theta) ^(2) = (1 + sec theta cosec theta) ^(2).

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

Prove that, 1/(costheta-cos3theta)+1/(costheta-cos5theta)+1/(costheta-cos7theta)+…+to n terms = 1/(2sintheta) [cottheta-cot(n+1)theta]

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

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

Prove that (cos(pi +theta)cos (-theta))/(cos(pi-theta) cos (pi/2+theta))=-cot theta

The base of a triangle is divided into three equal parts. If theta_(1), theta_(2), theta_(3) be thw angles subtended by these parts at the vertex, then prove that (cot theta_(1) +cot theta_(2) ) (cot theta_(2)+ cot theta_(3))=4 cosec ^(2) theta _(2)