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

Options

A. 4c
B. 2c
C. 7c
D. 3c

Answer

C

Explanation

We have, in `DeltaABC`
`("tan"(A)/(2))("tan"(B)/(2))=(3)/(4)`
`implies sqrt(((s-b)(s-c))/(s(s-a)))sqrt(((s-a)(s-c))/(s(s-b)))=(3)/(4)`
`implies sqrt(((s-b)(s-c)(s-a)(s-c))/(s(s-a)*s(s-b)))=(3)/(4)`
`implies((s-c))/(s)=(3)/(4)implies((a+b+c)/(2))/((a+b+c)/(2))=(3)/(4)`
`implies(a+b-c)/(a+b+c)=(3)/(4)`
`implies 4a+4b-4c=3a+3b+3c`
`implies a+b=7c`