Let tan x = (2ab)/(a2 – b2), where a > b > 0 and 0 < x < 90. Draw a right triangle with angle x and label two sides of the triangle to show tan x. Now find an expression for sin x.
sin x = (2ab)/c.
| c2 | = (a2 – b2)2 + (2ab)2 |
| = a4 – 2a2b2 + b4 + 4a2b2 | |
| = a4 + 2a2b2 + b4 | |
| = (a2 + b2)2 |
So c = a2 + b2, and sin x = (2ab)/(a2 + b2)