Question

In a ΔABC, cot `(("A - B")/2)* tan (("A + B")/2)` is equal to

Options

• `("a - b")/("a + b")`

• `("a + b")/("a - b")`

• `("a"("a - b"))/("b"("a + b"))`

• `("b - a")/("b + a")`

Answer 1

`("a + b")/("a - b")`

Explanation:

cot `(("A - B")/2)* tan (("A + B")/2)`

`= (cot (("A - B")/2))/(sin (("A - B")/2)) * (sin (("A + B")/2))/(sin (("A + B")/2))`

`= (2 sin (("A + B")/2) * cos (("A - B")/2))/(2 cos (("A + B")/2)*cos (("A - B")/2))`

`= (sin "A" + sin "B")/(sin "A" - sin "B")`

`("a + b")/("a - b")`    ....[By sine rule]