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tan theta + 2 tan 2 theta + 4 tan 4 thet...

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

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Solve tan theta + tan 2 theta + tan theta * tan 2 theta * tan 3 theta=1

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Prove that : tan 3 theta tan 2 theta tan theta= tan3 theta-tan 2 theta-tan theta .

Let theta in (0, pi/4) and t_(1)=tan theta)^(tan theta), t_(2)=(tan theta)^(cot theta), t_(3)=(cot theta)^(tan theta) and t_(4)=(cot theta)^(cot theta) , then show that t_(4) gt t_(3) gt t_(1) gt t_(2) .

General solution of tan theta+tan 4 theta+tan 7 theta=tan theta tan 4 theta tan 7 theta is

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

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

Prove that : tan 4 theta= (4 tan theta(1-tan^2 theta)) /(1-6 tan^2 theta+ tan^4 theta) .

Prove the following identity : sqrt (sec^2 theta+ cosec^2 theta)= tan theta+ cot theta= sec theta cosec theta .