Question

Find the Value of tanπ/8

Answer 1

π = 180°

tanπ/8
= tan 180/8
= tan 45/2
= tan 22.5°

tan (45/2) = √2-1

Answer 2

Answer:

Step-by-step explanation:

tanπ/8 = (sinπ/8)/(cosπ/8)

Multiply and divide by 2sinπ/8

tanπ/8 = 2(sinπ/8)(sinπ/8)/2(sinπ/8)(cosπ/8)

You might familiar with these formulas:

cos2x = 1-2sin^2x

sin2x = 2sinxcosx

Here, x = π/8

tanπ/8 = 1-cos2(π/8)/sin2(π/8)

= (1-cosπ/4)/(sinπ/4)

= (1-1/√2)/(1/√2)

= √2-1