tan pi8 sqrtAB A B Can someone please show me how to solve

tan pi/8 = (sqrtA)-B

A=?

B=?

Can someone please show me how to solve this?

tan(pi/8)

Use Trigonometric identity:

tan(x/2) = ( 1- cosx)/sinx

x = pi/4 ; cospi/4 = 1/sqrt2 and sinx = 1/sqrt2

So, tan( pi/8) = ( 1-1/sqrt2)/ 1/sqrt2

= ( sqrt2 -1)sqrt2/sqrt2

= sqrt2 -1

= SqrtA - B

A = 2 and B =1