Question

If a cosA = b cosB then prove that the triangle is either isosceles or right angled triangle

Answer 1

» Let's

=> a/sinA = b/sinB = c/sinC = K

=> a = KsinA

=> b = KsinB

=> c = KsinC

_________

» Now,

=> acosA = bcosB -____[GIVEN]

=> KsinA.cosA = KsinB.cosB

=> sinA.cosA = sinB.cosB

=> 2sinA.cosA = 2sinB.cosB

=> sin2A = sin2B

=> 2A = 2B _or_ => 2A = π-2B

=> A = B _or_ => A+B = π/2

=> A = B _or_ => C = π/2

=> BC = CA _or_ => C = π/2

_________________

» hence,

» ΔABC is either isosceles or right angled

________________[PROVED]

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_-_-_-_✌☆$BE \: \: \: \: BRAINLY$☆✌

Answer 2

ABC is an isosceles ∆ or a right angled ∆ at C

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