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If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠ A = ∠ B. plixxzxxxx
Dear StudentLet us assume the triangle ABC in which CD⊥ABGiven that the angles A and B are acute angles,such that cos (A) = cos (B)As per the angles taken,the cos ratio is written as AD/AC = BD/BCNow, interchange the terms, we getAD/BD = AC/BCLet take a constant valueAD/BD = AC/BC = kNow consider the equation asAD = k BD ...(1)AC = kBC ...(2)By applying Pythagoras theorem in△CAD and△CBD we get,CD^2 = BC^2 –BD^2... (3)CD^2 =AC^2−AD^2 ....(4)From the equations (3) and (4) we get,AC^^2−AD2= BC^2−BD^2Now substitute the equations (1) and (2) in (3) and (4)K^2(BC^2−BD^2)=(BC^2−BD^2) k^2=1Putting this value in equation, we obtainAC = BC∠A=∠B (Angles opposite to equal side are equal-isosceles triangle)Thanks
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