Pre Calculus

Question

Simplify the expression

 tan(1/2 x)+tan(1/8 x) 

1-tan(1/2 x)tan(1/8 x)

a) tan(-5x/8)

b) tan(5x/8

c) tan(-3x/8)

d) tan(3x/8)

Answer 1

[tan(1/2 x) + tan(1/8 x)] / [1 - tan(1/2 x)tan(1/8 x)]

 

 

This is an addition angle identity for tangent. 

 

tan(1/2 x  +  1/8 x) =

 

tan(4/8 x + 1/8 x) =

 

tan(5/8 x)