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

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Ashlee Arroyo

Mathematics

1 April, 12:19

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

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Plato · Answer 1

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)