Question

prove that tan 36+tan9+tan 36 tan9=1

Answer 1

Answer :

We know that,

tan45 = 1

⇒ tan (36 + 9) = 1

⇒ (tan36 + tan9)/(1 - tan36 tan9) = 1,

using the identity
tan(A + B) = (tanA + tanB)/(1 - tanA tanB)

⇒ tan36 + tan9 = 1 - tan36 tan9

⇒ tan36 + tan9 + tan36 tan9 = 1 [Proved]

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Answer 2

Refer above for the answer.