Question

express asin2C/2+csin2A/2interms of s, a, b, c

​

Answer 1

Answer:

Actually it is a wrong question. we can't prove this. It should be like this-

2{asin

2

2

C

+csin

2

2

A

}=(a+c−b)

so,now we will prove this-

as we know-

sin

2

θ=

2

1−cos2θ

now we will apply this formula in our question-

L.H.S.

=2{asin

2

2

C

+csin

2

2

A

}

=2

⎩

⎪

⎪

⎨

⎪

⎪

⎧

a

⎝

⎜

⎜

⎛

2

1−cos2×

2

C

⎠

⎟

⎟

⎞

+c

⎝

⎜

⎜

⎛

2

1−cos2×

2

A

⎠

⎟

⎟

⎞

⎭

⎪

⎪

⎬

⎪

⎪

⎫

=a(1−cosC)+c(1−cosA)

=a+c−(acosC+ccosA)

here we will apply cosine rule⇒(acosC+ccosA)=b

=a+c−b

=R.H.S.