Question Number 209 by 02@>@0 last updated on 25/Jan/15
$${y}={sin}\left({x}\right)+{cos}\left({x}\right) \\ $$
Answered by 123456 last updated on 15/Dec/14
$${y}=\frac{\sqrt{\mathrm{2}}}{\:\sqrt{\mathrm{2}}}\mathrm{sin}\:{x}+\frac{\sqrt{\mathrm{2}}}{\:\sqrt{\mathrm{2}}}\mathrm{cos}\:{x} \\ $$$${y}=\sqrt{\mathrm{2}}\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\mathrm{sin}\:{x}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\mathrm{cos}\:{x}\right) \\ $$$${y}=\sqrt{\mathrm{2}}\left(\mathrm{cos}\:\frac{\pi}{\mathrm{4}}\mathrm{sin}\:{x}+\mathrm{sin}\:\frac{\pi}{\mathrm{4}}\mathrm{cos}\:{x}\right) \\ $$$${y}=\sqrt{\mathrm{2}}\mathrm{sin}\:\left({x}+\frac{\pi}{\mathrm{4}}\right) \\ $$