Question

if cos A + sin A = √2 cos A then cos A- sin A

Answer 1

If Cos A + Sin A = √2 Cos A then Cos A - Sin A = √2 sin A.




Solution :-

We have :

=> Cos A + Sin A = √2 Cos A


Squaring both sides , we get


=> ( CosA + SinA)² = 2Cos²A


=> Cos²A + Sin a + 2Cos A SinA = 2 Cos²A


=> Cos²A - 2 Cos A Sin = Sin²A


=> Cos²A - 2 Cos A Sin + Sin²A = Sin²A + Sin²A [ Adding Sin²A on both sides ]



=> ( Cos A - Sin A )² = 2 Sin²A



=> ( Cos A - Sin A ) = √2 Sin A .


Hence,

( Cos A - Sin A ) = √2 Sin A.