Question

In Δ ABC, with the usual notations, if `(tan  "A"/2)(tan  "B"/2) = 3/4` then a + b = ______.

Options

• 4c

• 2c

• 7c

• 3c

Answer 1

In Δ ABC, with the usual notations, if `(tan  "A"/2)(tan  "B"/2) = 3/4` then a + b = 7c.

Explanation:

We have, In Δ ABC

`(tan  "A"/2)(tan  "B"/2) = 3/4`

`=> sqrt((("s - b")("s - c"))/("s"("s - a"))) sqrt((("s - a")("s - c"))/("s"("s - b"))) = 3/4`

`=> sqrt((("s - b")("s - c")("s - a")("s - c"))/("s"("s - a")* "s"("s - b"))) = 3/4`

`=> ("s - c")/"s" = 3/4`

`=> (("a + b + c")/2 - "c")/(("a + b + c")/2) = 3/4`

`=> ("a + b - c")/("a + b + c") = 3/4`

⇒ 4a + 4b - 4c = 3a + 3b + 3c

⇒ a + b = 7c