trigonometric identities

Question

Use trigonometric identities to find the exact value of tan(5π/8).

Answer 1

Tan(5π/8) = Tan [(5π/4)/2]

 

Tan(θ/2) = ±√{(1 - cosθ)/(1 + cosθ)}

 

Since 5π/8 lies in quadrant 2, tan (5π/8) < 0

 

tan (5π/8)=tan[(5π/4)/2)=-√{(1 - cos(5π/4))/(1 + cos(5π/4))}

 

                                                = -√{(1 + √2/2)/(1 - √2/2)}

 

                                                = -√{(2 + √2)/(2 - √2)}