Question

tan 36° + tan 9° + tan 36 tan 9° = 1​

Answer 1

Step-by-step explanation:

we know

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]