Question Number 46402 by scientist last updated on 25/Oct/18
$${show}\:{that}\:\mathrm{cos}\:\mathrm{7}\frac{\mathrm{1}}{\mathrm{2}}\:=\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}+\sqrt{\mathrm{4}}+\sqrt{\mathrm{6}} \\ $$
Commented by Meritguide1234 last updated on 25/Oct/18
$${it}\:{should}\:{be}\:{cot}\mathrm{7}\frac{\mathrm{1}}{\mathrm{2}} \\ $$
Answered by ajfour last updated on 25/Oct/18
$$\mathrm{cos}\:\mathrm{15}°=\sqrt{\frac{\mathrm{1}+\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}}{\mathrm{2}}}=\:\frac{\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}}{\mathrm{2}} \\ $$$$\mathrm{cos}\:\left(\frac{\mathrm{15}}{\mathrm{2}}\right)^{°} =\:\sqrt{\frac{\mathrm{1}+\frac{\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}}{\mathrm{2}}}{\mathrm{2}}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\frac{\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}}}{\mathrm{2}}\:. \\ $$