Question

cosa-sina=√2sina ho to prove that cosA+sona=√2cosa

Answer 1

CosA - SinA=/2sinA

Squaring both sides we get

(CosA - SinA)²=(/2SinA)²

Cos²A + Sin²A - 2SinA.CosA=2Sin²A

Cos²A=2Sin²A - Sin²A + 2SinA.CosA

Adding Cos²A on both sides we get

2Cos²A=Cos²A + Sin²A + 2SinA.CosA

(CosA + SinA)²=(/2cosA)²

Comparing both sides

CosA+SinA=/2CosA

Hence proved

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