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Prove the identity (sina-cosatanb)/(cosa+sinatanb) = tan (a+b)

Prove the identity (sina-cosatanb)/(cosa+sinatanb) = tan (a+b)
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Prove the identity (sina-cosatanb)/(cosa+sinatanb) = tan (a+b)

User Brennan Cheung
by
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1 Answer

5 votes
sina - (cosa)(tanb)/cosa + (sina)(tanb)
sina ≡ (tana)(cosa)

(tana)(cosa) - (cosa)(tanb)/cosa + (tana)(cosa)(tanb)
= cosa(tana - tanb)/cosa(1 + tanatanb)
(cosas cancel out)
= (tana - tanb)/(1 + tanatanb) ≡ tan(a-b)
User Venomy
by
8.3k points
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