Question

Prove that,tan 55 - tan 35=2tan20
​

Answer 1

Given :  tan 55 - tan 35=2tan20

To Find : prove that

Solution:

 55 = 20 + 35

=> 20  = 55 - 35

taking Tan both sides

=> Tan 20 = Tan ( 55 - 35)

=> Tan 20  = (Tan 55 - Tan 35) /(1 + Tan55 . Tan35)

Tan35 = Cot55 = 1/tan55 => Tan55 . Tan35 =1

=> Tan 20  = (Tan 55 - Tan 35) /(1 + 1)

=> Tan 20  = (Tan 55 - Tan 35) /2

=> 2 Tan 20  = Tan 55 - Tan 35

=> Tan 55 - Tan 35 = 2 Tan 20  

QED

Hence Proved

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