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Q)

In a $\Delta$ABC if the sides are $a=3,b=5,c=4$ then $\sin\large\frac{B}{2}$$+\cos{\large\frac{B}{2}}$ is equal to

$\begin{array}{1 1}(a)\;a^2&(b)\;b^2\\(c)\;c^2&(d)\;None\;of\;these\end{array}$

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A)
Given : $a=3$
$b=5$
$c=4$
$\Rightarrow a^2+b^2=c^2$[By pythogorus theorem]
$\Rightarrow 3^2+4^2=5^2$
$\Rightarrow 9+16=25$
$25=25$
Angle is $90^{\large\circ}$.Hence it is right angled $\Delta$le.$\angle B=90^{\large\circ}$
$\sin\large\frac{B}{2}$$+\cos\large\frac{B}{2}$$=\sqrt 2$
Hence (d) is the correct option.
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