Question

What is the Name of Formula of this Question Answer ?

Answer 1

Answer:

Tan 45 can be written as Tan ( 35 + 10 )

So the formula used here is:

$Tan ( A + B ) = \dfrac{ Tan A + Tan B}{1 - TanA.TanB}$

This is also called as Sum of Angles Formula.

Solving the sum further we get,

$\implies Tan \:\:45 = \dfrac{ Tan 35 + Tan 10}{1 - Tan35.Tan 10} \\ \\ \implies 1 = \dfrac{ Tan 35 + Tan 10}{1 - Tan 35.Tan10} \\ \\ \\ \text{ Cross multiplying the term we get,} \\ \\ \implies 1 ( 1 - Tan35.Tan10 ) = Tan 35 + Tan 10 \\ \\ \text{ Transposing Tan 35 and Tan 10 terms to the RHS we get,} \\ \\ \implies 1 = Tan35 + Tan10 + Tan35.Tan10 \\ \\ \boxed{ Hence \:\: Proved}$

Hope my answer helped !