UPSC NDA Math Model Paper 5

Given: For ΔABC we have a = 3, b = 5 and c = 6
Here, we have to find the value of cos (B/2)
As we know that, if a, b and c are the sides of the Δ ABC then 2S = a + b + c
⇒ 2S = 3 + 5 + 6 = 14
⇒ S = 7
As we know that, cos‌

B

2

=√

S(S−b)

ca

⇒cos‌

B

2

=√

7×(7−5)

6×3

=

√7

3

Hence, option D is the correct answer.