Question

In a ΔABC, 2ab sin`((A + B - C)/2)` = ______

Options

• a² + b² - c²

• b² - c² - a²

• c² + a² - b²

• c² - a² - b²

Answer 1

In a ΔABC, 2ab sin`((A + B - C)/2)` = a² + b² - c²

Explanation:

`2ab sin((A + B - C)/2) = 2ab sin((A + B + C - 2C)/2)`

= 2ab sin`((pi - 2C)/2)` ...............[∵ A + B + C = π]

= 2ab sin`(pi/2 - C)`

= 2ab cos C 

= a² + b² - c² .........................[by cosine rule]