Question

ABC is a right angle triangle, with ∠B = 90°. If (AB -
BC)2 = 2BC(AC - BC), then ∠C =

Answer 1

Answer:

Step-by-step explanation:

(AB - BC)² = 2BC ( AC - BC)

in Δ ABC  ∠B = 90°

AB = AC SinC

BC = AC CosC

=> (AC SinC  - AC CosC)² = 2(AC CosC)(AC - AC CosC)

=> AC² (SinC - CosC)² = 2AC² CosC(1 - CosC)

=>  Sin²C + Cos²C - 2SinCCosC = 2CosC(1 - CosC)

=> 1  - 2SinCCosC = 2CosC(1 - CosC)

=>  1 =  2CosC(1 + SinC - CosC)

=> CosC(1 + SinC - CosC) = 1/2