Tan 5pi/8 exact value

To solve this exercirse, you must apply the proccedure below:

1. You need to apply the "Half-angle identity for tangent", which is:

Tan (θ/2) = Sinθ/1+Cos θ

2. But first, the angle 5 π/4 must be expressed as a product of 1/2, as below:

5π/8 = (5π/4) (1/2)

3. Now, you can susbtitute the angle into the formula:

=Sinθ/1+Cosθ

=Sin (5π/4) / 1+Cos (5π/4)

Sin (5π/4) = - √2/2

Cos (5π/4) = Cos (π/4)

π/4 is the reference angle of 5π/4

π/4=√2/2

4. Then:

= (-√2/2) / (1-√2/2)

5. When you simplify the expression, you obtain:

=-1-√2

6. Therefore, the answer is: - 1-√2