Question

Cos a + sin a=root2cos a then show cos a -sin a =root2sina
From which book this question is ????

Answer 1

$\pink{\underline{Hey\:mate !\:your \: Solution}}$

Squaring both sides

$(cos A + sin A)^{2} = (\sqrt{2} cos A)^{2}\\\implies cos^{2} A + sin^{2} A + 2cos A\times sin A = 2\times cos^{2} A\\\implies 1 + 2cos A\times sin A = 2 cos^{2} A\\\implies 1 + 2cos A\times sin A = 2 - 2sin^{2} A \\\implies 2sin^{2} A = cos^{2} A + sin^{2} A-2cos A\times sin A \\\implies (cos A - sin A)^{2} = 2 sin^{2}A \\\implies cos A - sin A = \sqrt{2 sin^{2} A}\\\implies cos A - sin A = \sqrt{2} sin A$