Question

In a triangle ABC,prove that b cos^2C/2+c cos^2B/2=s

Answer 1

i hope this will usful to u

Answer 2

Answer:

L.H.S = R.H.S

Step-by-step explanation:

In this question

Given that

$b\times cos^2(\frac{C}{2}) + c\times cos^2(\frac{B}{2})$ = s

Formula,

2s = a + b + c

$cos^2(\frac{C}{2})$ = $\frac{s\times (s - c)}{ab}$

$cos^2(\frac{B}{2})$ = $\frac{s\times (s - b)}{ac}$    

Now we take R.H.S

$b\times cos^2(\frac{C}{2}) + c\times cos^2(\frac{B}{2})$

$b\times \frac{s\times (s - c)}{ab}$ +  $c\times \frac{s\times (s - b)}{ac}$            

$\frac{s\times (s - c)}{a}$ +  $\frac{s\times (s - b)}{a}$  

$\frac{s}{a}\times (s - c + s - b)$

$\frac{s}{a}\times (2s - c - b)$

$\frac{s}{a}\times (a+ b + c - c - b)$

$\frac{s}{a}\times (a)$

s

L.H.S

Hence, L.H.S = R.H.S