if tan 2 theta tan 4 theta =1 then find value of tan 3 theta - Maths - Introduction to Trigonometry

Question

if tan 2 theta tan 4 theta =1 then find value of tan 3 theta

Lovina Kansal · Accepted Answer

Dear student
Given:tan2θ tan4θ=1⇒tan2θ=1tan4θ⇒tan2θ=cot4θ      
(1)We know that tan(90+x)=-cotxSo, cot4x=-tan(90+4x)    
(2)So, from (1) and (2), we get2θ=-(90+4θ)⇒6θ=-90⇒3θ=-45So, tan3θ=tan(-45)⇒tan3θ=-tan45⇒tan3θ=-1
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if tan 2 theta.tan 4 theta =1 then find value of tan 3 theta