Observe the following statements: (I) In `!ABC,bcos^(2)C/2+ccos^(2)B/2=s` , (II) In `!ABCcotA/2=(b+c)/2rArrB=90^(@)`
Which of the following is correct?

Options

A. both I and II are true
B. I is true, II is false
C. I is false, II is true
D. both I and II are false

Explanation

We have
`bcos^(2)C/2+ccos^(2)B/2=b(s(s-c))/(ab)+c(s(s-b))/(ac)=s/a(2s-b-c)=s`
So, statement-I is true.
Now, `cotA/2=(b+c)/a`
`rArr(cotA/2)/(sinA/2)=(sinB+sinC)/(sinA)`
`rArr(cosA/2)/(sinA/2)=(2sin(B+C)/2cos(B-C)/2)/(2sinA/2cosA/2)`
`rArrcosA/2=cos(B-C)/2`
`rArrA/2=(B-C)/2rArrA+C=BrArr2B=180^(@)rArrB=90^(@)`
But statement-II is cot`A/2=(b+c)/2`
So, statement-II is not true.