Writing Trig Fuunctions

Question

Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number.

tan pi/24 + tan pi/8/ 1 - tan pi/24tan pi/8

Find its exact value?

Answer 1

Hi Harris,

Thanks for your question!

For this question, we want to use the Sum-of-Angles identity for tangent:

tan(x+y) = [ tan(x) + tan(y) ]/[ 1 - tan(x)tan(y) ].

Here, x = pi/24 and y = pi/8. Using this identity, we find

[ tan(pi/24) + tan(pi/8) ]/[ 1 - tan(pi/24)tan(pi/8) ] = tan(pi/24 + pi/8) = tan(pi/6).

But, tan(pi/6) = sin(pi/6)/cos(pi/6) = [ 1/2 ]/[ sqrt(3)/2 ] = sqrt(3)/3, which is our final answer.