Question

How do you use the double angle formula to determine tan 300?

Answer 1

Use the trig identity: `tan 2a = (2tan a)/(1 - tan^2 a)`
tan 2a = 300 deg

`tan a = tan (150) = -(sqr3)/3 = -0.577 -> 2tan a = 1. 154`

`1 - tan^2 (150) = (1 - 0.33) = 0.667`

`tan 300 = 1.154/0.667 = 17.3`

Note. Select sign (+) because 300 deg is inside Quadrant III. tan 300 is positive.

Check with calculator.
tan 300 = 17.32.