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Question Number 38288 by ajfour last updated on 23/Jun/18

tan α−tan β = 2tan θ  asin α−bsin β = lsin θ  express sin α, sin β  in terms of 𝛉.

tanαtanβ=2tanθasinαbsinβ=lsinθexpresssinα,sinβintermsofθ.

Answered by tanmay.chaudhury50@gmail.com last updated on 24/Jun/18

t_1 =tan(α/2)   t_2 =tan(β/2)   p=tan(θ/2)  ((2t_1 )/(1−t_1 ^2 ))−((2t_2 )/(1−t_2 ^2 ))=((4p)/(1−p^2 ))  a((2t_1 )/(1+t_1 ^2 ))−b((2t_2 )/(1+t_2 ^2 ))=l((2p)/(1+p^2 ))  wait

t1=tanα2t2=tanβ2p=tanθ22t11t122t21t22=4p1p2a2t11+t12b2t21+t22=l2p1+p2wait

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