Question

tan 9° + tan 36° + tan 9° tan 36° now find value options are 1)0 , 2)1/√3 , 3)√3 , 4)1
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Answer 1

Step-by-step explanation:

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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