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

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

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

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

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

Prove that: a) cotthetacot(60^(@)-theta)cot(60^(@)+theta)=cot3theta b) cos5theta=16cos^(5)theta-2thetacos^(3)theta+5costheta c) sin4theta=4sinthetacos^(3)theta-4costhetasin^(3)theta

Prove that: ("cosec" theta + cot theta)/("cosec" theta - cot theta) = ("cosec" theta + cot theta )^(2) = 1 + 2 cot^(2) theta + 2 "cosec" theta cot theta .

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