Prove that `cot theta cot 2 theta+ cot 2 theta cot 3 theta+ 2= cot theta (cot theta- cot 3 theta)`.

tan theta + 2 tan 2 theta + 4 tan 4 theta + 8 cot 8 theta = cot theta.

Prove that (1 +cot theta -cosec theta )(1+tan theta +sec theta )=2.

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

(cosec theta -sin theta ) (sec theta - cos theta ) (tan theta + cot theta ) = 1.

Prove the following : cot 4 theta(sin 5 theta+ sin 3 theta)=cot theta(sin 5 theta-sin 3 theta) .

Prove the following identity : cot^2 theta- cos^2 theta= cot^2 theta cos^2 theta .

The base of a triangle is divided into three equal parts. If theta_(1), theta_(2), theta_(3) be the 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)

If a tower subtends angles theta, 2 theta and 3 theta at three points A,B,and C respectively, lying on the same side of a horizontal line through the foot of the tower, show that (AB)/(BC) (cot theta- cot 2 theta)/(cot 2 theta - cot 3 theta).

If : cot theta + cot((pi)/4 + theta) = 2 , then : theta =

Prove the following identity : (sin theta)/(1+cos theta)+ (tan theta)/(1+cos theta)= sec theta cosec theta- cot theta .