# mathematics

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in triangle abc if acosA= bcosB then how to prove the triangle is isosceles or right angled

• mathematics -

we know that a/sinA = b/sinB
if acosA = bcosB, then
a/cosB = b/cosA

b = acosA/cosB
b = asinB/sinA

so, acosA/cosB = asinB/sinA
cosAsinA = sinBcosB
sin2A = sin2B

means A=B and the triangle is isoceles

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