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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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