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

Options

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.

Explanation

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.