Question

prove tan 45/2 = √2-√2​

Answer 1

Answer:

Step-by-step explanation:

tan(45°) = tan(45°/2 + 45°/2)

= 2tan(45°/2)÷(1 - tan^2(45°/2))

(Using expansion for tan(2x))

This implies, 1 = 2tan(45°/2)÷(1 - tan^2(45°/2))

Rearranging terms, tan^2(45°/2) + 2tan(45°/2) - 1 = 0

Solving the quadratic equation x^2 + 2x - 1 = 0 gives

x = (2^(1/2) - 1) or (- 2^(1/2) - 1)

But tan(45°/2) lies in the first quadrant, therefore it should be positive.

tan(45°/2) = (2^(1/2) - 1)

Answer 2

I think I help you ok bey you don't know question then ask me