Question

If $\cos A+\sin A=\sqrt{2}\cos ({90}^o-A)$, find the value of $\sin A-\cos A$

Answer 1

$\cos A+\sin A=\sqrt{2}\cos (90-A)$

$\cos A+\sin A=\sqrt{2}\sin A$

$\cos A=\sqrt{2}\sin A-\sin A$

$\cos A=(\sqrt{2}-1)-\sin A$

$\cos A=\sin A(\sqrt{2}-1)$

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

$\cos A=\sin A\frac{(2-1)}{\sqrt{2}+1}$

$\sqrt{2}\cos A+\cos A=\sin A$

$\cos A-\sin A=\sqrt{2}\cos A$