Use the figure to find the exact value of the following trig

Use the figure to find the exact value of the following trigonometric function 15 tan (20) 12 tan (20)-U (Simplify your answer.)

Solution

tan(theta) = 9/12 or 3/4

We know
tan(2theta) = 2tan(theta) / (1 - tan^2theta)

= 2(3/4) / (1 - (3/4)^2)

= (3/2) / (1 - 9/16)

= (3/2) / (7/16)

= 3/2 * 16/7

= 3 * 8/7

= 24/7 ----> ANS