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If a,b,c are the sides of triangle of angle A,B,C,opposite to it respectively and given that: Sin(A-B)=(a/a+b)sinAcosB-(b/a+b)cosAsinB then prove that the triangle is isosceles

If a,b,c are the sides of triangle of angle A,B,C,opposite to it respectively and
given that:
Sin(A-B)=(a/a+b)sinAcosB-(b/a+b)cosAsinB
then prove that the triangle is isosceles

Grade:12

1 Answers

Himanshu
103 Points
5 years ago
Sin(A-B)=(a/a+b)sinAcosB-(b/a+b)cosAsinB
> sinA.cosB – cosA.sinB = (a/a+b)sinAcosB-(b/a+b)cosAsinB
Comparing both sides.
a/a+b = 1          …i)
b/a+b = 1          …ii)
From i) and ii) ,
a/a+b = b/a+b
a = b
Hence, the triangle is isosceles.

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