Question

If A + B = 450, show that

(1 tan )(1 tan ) 2 + + = A B .​

Answer 1

Answer:

tan(A+B)

→ 1 = (tanA+tanB) / (1 - tanAtanB)

→ 1 - tanAtanB = tanA + tanB

→ 2 = tanA + tanB + tanAtanB + 1

→ 2 = (1 + tanA)(1 + tanB)

QED.

Plug A = B = pi/8 in the above equation... A+B = pi/4 = 45°.

2 = (1 + tan pi/8)²

→ sqrt2 = 1 + tan pi/8

→ tan pi/8 = sqrt2 - 1.