If Cos A + Sin A = $$\sqrt{2}$$ Cos A then Cos A- Sin A is equal to: (Where $$0^\circ$$<A<$$90^\circ$$)

Given : $$cos A+sin A=\sqrt2 cos A$$

Squaring both sides, we get :

=> $$(cos A+sin A)^2=(\sqrt2 cos A)^2$$

=> $$cos^2A+sin^2A+2sin A.cos A=2cos^2A$$

=> $$1+2sin A.cos A=2(1-sin^2A)$$

=> $$1+2sin A.cos A=2cos=2-2sin^2A$$

=> $$2sin A.cos A=2cos=1-2sin^2A$$ -----------------(i)

To find : $$cos A-sin A=x$$

Squaring both sides, we get :

=> $$x^2=cos^2A+sin^2A-2sin A.cos A$$

Substituting value from equation (i),

=> $$x^2=1-(1-2sin^2A)$$

=> $$x^2=2sin^2A$$

=> $$x=\sqrt{2sin^2A}$$

=> $$x=\sqrt2sin A$$

=> Ans - (C)