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In any DeltaABC,("tan"(A)/(2)-"tan"(B)/(...

In any `DeltaABC,("tan"(A)/(2)-"tan"(B)/(2))/("tan"(A)/(2)+"tan"(B)/(2))` is equal to

A

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

B

`(a-b)/(c)`

C

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

D

`(c)/(a+b)`

Text Solution

Verified by Experts

The correct Answer is:
B
`("tan"(A)/(2)-"tan"(B)/(2))/("tan"(A)/(2)+"tan"(B)/(2))=(sqrt(((s-b)(s-c))/(s(s-a)))-sqrt(((s-a)(s-c))/(s(s-b))))/(sqrt(((s-b)(s-c))/(s(s-a)))+sqrt(((s-a)(s-c))/(s(s-b))))`
`=((s-b)sqrt(s(s-c))-(s-a)sqrt(s(s-c)))/((s-b)sqrt(s(s-c))+(s-a)sqrt(s(s-c)))`
`=(sqrt(s(s-c))(s-b-s+a))/(sqrt(s(s-c))(s-b+s-a))=(a-b)/(c)`
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