Question Number 192346 by Rupesh123 last updated on 15/May/23
Answered by som(math1967) last updated on 15/May/23
$$\left(\frac{\mathrm{2}{cos}\mathrm{30}{cos}\mathrm{20}+{cos}\mathrm{70}+{cos}\left(\mathrm{180}−\mathrm{70}\right)}{{cos}\mathrm{20}}\right)^{\mathrm{8}} \\ $$$$=\left(\frac{\sqrt{\mathrm{3}}{cos}\mathrm{20}+\mathrm{cos}\:\mathrm{70}−\mathrm{cos}\:\mathrm{70}}{{cos}\mathrm{20}}\right)^{\mathrm{8}} \\ $$$$=\left(\frac{\sqrt{\mathrm{3}}{cos}\mathrm{20}}{{cos}\mathrm{20}}\right)^{\mathrm{8}} \\ $$$$=\left(\sqrt{\mathrm{3}}\right)^{\mathrm{8}} =\mathrm{81} \\ $$