Prove that `1+cot theta <= cot (theta/2) `for `0 < theta < pi`. Find `theta` when equality signs holds.

Using Pythagoras theorem, prove that 1 + cot^2 theta = cosec^2 theta,

Prove that 1+cot^(2) theta = cosec^(2) theta

Prove that 1+cot^(2) theta = cosec^(2) theta

If theta+phi=45^@ , prove that (cot theta-1) (cot phi-1) =2 .

Prove that (cot theta+csc theta-1)/(cot theta-csc theta)=(cot theta+csc theta)(cot theta+csc theta-1)

Prove that cot theta + cot (60^(@) theta) + cot (120^(@) + theta) = 3 cot 3 theta .

If theta+phi=45^(@) ,prove that (cot theta-1)(cotphi-1)=2

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)

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)

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)