in triangle ABC , if a2tanB=b2 tanA, then prove that the triangle is either right triangle or isosceles - Maths -

Question

in triangle ABC , if a2tanB=b2 tanA, then
prove that the triangle is either right triangle or isosceles

Neha Sethi · Accepted Answer

Dear student

asinA=bsinB=csinC=k⇒a=ksinA , b=ksinB , and c=ksinC Now, a2tanB=b2tanAa2sinBcosB=b2sinAcosAa2cosAsinB=b2sinAcosBk2sin2AcosAsinB=k2sin2BsinAcosB2sinAcosA=2sinBcosB2sinAcosA-2sinBcosB=0sin2A=sin2B2A=2BSo triangle formed is isosceles triangleA=B
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in triangle ABC , if a2tanB=b2 tanA, then prove that the triangle is either right triangle or isosceles.

in triangle ABC , if a²tanB=b²tanA, then prove that the triangle is either right triangle or isosceles.