**How do you evaluate tan (pi/12) using the half angle formula?**

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## Question “How do you evaluate tan (pi/12) using the half angle formula?”

How do you evaluate tan (pi/12) using the half angle formula?

## Answer

2 – sqrt3

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Explanation:

Use the trig identification:

tan 2a = (2tan a)/(1 – tan^2 a)

Trig table –->

tan 2a = tan (pi/6) = 1/sqrt3

We get:

1/sqrt3 = (2t)/(1 – t^2).

(1-t2) = 2sqrt3

t^2 + 2sqr3t – 1 = 0

This quadratic equation can be solved for t.

D = d2 + 4ac = 3(3) + 4 = 16

d = +-4

There are two real roots to this:

t = tan (pi/12) = -b/(2a) +- d/(2a) = -(2sqrt3)/2 +- 4/2 = – sqrt3 +- 2

Since

tan (pi/12)

tan (pi/12) = 2 – sqrt3

Calculator

tan (pi/12) = tan 15^@ = 0.27

2 – sqrt3 = 2 – 1.73 = 0.27

## Conclusion

Above is the solution for “**How do you evaluate tan (pi/12) using the half angle formula?**“. We hope that you find a good answer and gain the knowledge about this topic of **trigonometry**.