Question

For ΔABC, express $a\ sin^{2}(\frac{C}{2})\ +\ c\ sin^{2}(\frac{A}{2})$ in terms of s, a, b, and c.

Answer 1

Solution :

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We know that ,

sinC/2 = √[(s-a)(s-b)]/ab

SinA/2 = √[(s-b)(s-c)]/2

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Now ,

asin²C/2 + cSin²A/2

=a × [(s-a)(s-b)]/ab + c × [(s-b)(s-c)]/bc

= [(s-a)(s-b)]/b + [(s-b)(s-c)]/b

= [(s-b)/b ] ( s - a + s - c )

= [(s-b)/b ] ( 2s - a - c )

= [ (s-b)/b ] ( a + b + c - a - c )

[ Since , 2s = a + b + c ]

= [ ( s - b )/b ] × b

= s - b

Answer 2

HELLO DEAR,

Answer:

Step-by-step explanation:

We know that ,

sinC/2 = √[(s-a)(s-b)]/ab

SinA/2 = √[(s-b)(s-c)]/2

Now ,

asin²C/2 + cSin²A/2

=> a * [(s-a)(s-b)]/ab + c × [(s-b)(s-c)]/bc

=> [(s-a)(s-b)]/b + [(s-b)(s-c)]/b

=> [(s-b)/b ] ( s - a + s - c )

=> [(s-b)/b ] ( 2s - a - c )

=> [ (s-b)/b ] ( a + b + c - a - c )

[ we know, 2s = a + b + c ]

=> [ ( s - b )/b ] * b

=> s - b

I HOPE IT'S HELP YOU DEAR,

THANKS