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Statement-1: In a !ABC, (a+b+c)(tanA/2...

Statement-1: In a `!ABC`,
`(a+b+c)(tanA/2+tanB/2)=2c cotC/2`
Statement-2: In a `!ABC`, a = b cos C + c cos B

A

Statement-1 is True, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.

B

Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.

C

Statement-1 is True, Statement-2 is False.

D

Statement-1 is False, Statement- 2 is True.

Text Solution

Verified by Experts

Clearly, statement- 2 is true. (see projection formulae in theory)
Now,
`(a+b+c)(tanA/2+tanB/2)`
`=2s{(Delta)/(s(s-a))+(Delta)/(s(s-b))}`
`(2Delta)/((s-a)(s-b))(2s-a-b)=(2Deltac)/((s-a)(s-b))`
`=2csqrt((s(s-c))/((s-a)(s-b)))=2ccotC/2`
So, statement-1 is also true.
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