If `0ltthetaltpi,` prove that `cot\ theta/2ge1+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)

If sin(theta+alpha)=n sin(theta-alpha) , prove that cot theta=(n-1)/(n+1) cot alpha .

Prove that : cot theta-tan theta=2cot2 theta

Prove that cot theta-tan theta=2cot 2 theta .

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

If "cot" theta "cot" 7 theta + "cot" theta "cot" 4 theta + "cot" 4 theta "cot" 7 theta = 1, " then" theta =

Prove cos ec^(2)theta=1+cot^(2)theta

Prove that cosec 2alpha = cot alpha - cot 2alpha . Hence or otherwise prove that cosec theta + cosec 2theta + cosec 4theta + cosec 8theta = cot theta/2 - cot 8theta .

Prove that: cot theta cot2 theta+cot2 theta cot3 theta+2=cot theta(cot theta-cot3 theta)

Show that cot theta* cot 2theta+ cot 2theta *cot 3theta + 2 = cot theta(cot theta - cot 3theta)