Question

In triangle ABC , if the sides are a=3, b =5 and c = 4, then sinB/2 +cosB/2 ?

Answer 1

`sqrt2.`

Explanation:

Note that, `a^2+c^2=b^2.`

Hence, by the Converse of Pythagoras Theorem, `B=90^@.`

`sin(B/2)+cos(B/2)=sin45^@+cos45^@=1/sqrt2+1/sqrt2.`

`rArr sin(B/2)+cos(B/2)=2/sqrt2=sqrt2.`