Question Number 31548 by de best last updated on 10/Mar/18
$${simplify}\:{cosx}\:+\:\sqrt{\mathrm{3}}{sinx}\:{as}\:{a}\: \\ $$$${single}\:{trigonometry}\:{ratio} \\ $$
Answered by $@ty@m last updated on 10/Mar/18
$$\mathrm{cos}\:{x}+\sqrt{\mathrm{3}}\mathrm{sin}\:{x} \\ $$$$=\mathrm{2}\left(\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:{x}+\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\mathrm{sin}\:{x}\right) \\ $$$$=\mathrm{2}\left(\mathrm{sin}\:\mathrm{30cos}\:{x}+\mathrm{cos}\:\mathrm{30sin}\:{x}\right) \\ $$$$=\mathrm{2sin}\:\left({x}+\mathrm{30}\right) \\ $$