If (a^(2)+b^(2))/(a^(2)-b^(2))=(sinC)/(s...

If `(a^(2)+b^(2))/(a^(2)-b^(2))=(sinC)/(sin(A-B))` , then S.T . `DeltaABC` is either isoceles or right angled triangle .

Answer

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If (a^2 +b^2)/( a^2 - b^2) = ( sin C)/( sin (A -B) ) , prove that Delta ABC is either isosceles or right angled.

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Knowledge Check

If ( a^(2) + b^(2))/( a^(2) - b^(2)) = ( sin C)/( sin (A- B)) then triangle ABC is

A

Scalene

B

Equilateral

C

Isosceles

D

Right angled

In DeltaABC=(b^(2)+c^(2))/(b^(2)-c^(2))=(Sin(B+C))/(Sin(B-C)) then the triangle is

A

Right-angled

B

isosceles

C

right angled or isosceles

D

Scalene

In a triangle ABC if (a^(2) + b^(2))/(a^(2) - b^(2)) sin (A - B) = 1 and the triangle is not right angled, then cos (A - B) =

A

`sin (C/2 - pi/4)`

B

`cos (C/2 - pi/4)`

C

`tan(C/2 - pi/4)`

D

`cot (C/2 - pi/4)`

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In a DeltaABC " if " a cosA=bcosB the prove that triangle is either isosceles or right angled .

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I: In a Delta ABC, if (a+b+c) (a+b-c)=ab then angle C=60^@ II: IF sin^2 A+ sin^2 B + sin^2 C=2 in a Delta ABC then it is right angled triangle

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