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. tan theta/2 tan theta/2 = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Solution

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

tan(theta) = 16/12 = 4/3

2(1-tan^2(theta/2)) = 3tan(theta/2)

2tan^2(theta/2)+3tan(theta/2)-2 = 0

2tan^2(theta/2)+4tan(theta/2)-tan(theta/2)-2 = 0

2tan(theta/2)[tan(theta/2)+2] -1[tan(theta/2)+2] = 0

tan(theta/2) = -2,1/2