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Category: Algebra

Question-62112

Question Number 62112 by aliesam last updated on 15/Jun/19 Answered by MJS last updated on 15/Jun/19 $$\mathrm{sin}^{\mathrm{10}} \:{x}\:+\mathrm{cos}^{\mathrm{10}} \:{x}\:=\frac{\mathrm{11}}{\mathrm{36}} \\ $$$$\frac{\mathrm{5}}{\mathrm{128}}\mathrm{cos}\:\mathrm{8}{x}\:+\frac{\mathrm{15}}{\mathrm{32}}\mathrm{cos}\:\mathrm{4}{x}\:+\frac{\mathrm{63}}{\mathrm{128}}=\frac{\mathrm{11}}{\mathrm{36}} \\ $$$$\mathrm{cos}\:\mathrm{8}{x}\:+\mathrm{12cos}\:\mathrm{4}{x}\:+\frac{\mathrm{43}}{\mathrm{9}}=\mathrm{0} \\ $$$${x}=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{arctan}\:{t}…

Question-127641

Question Number 127641 by Study last updated on 31/Dec/20 Answered by Dwaipayan Shikari last updated on 31/Dec/20 $$\mathrm{1}.\mathrm{2}.\mathrm{3}.\mathrm{4}.\mathrm{5}…={e}^{−\zeta'\left(\mathrm{0}\right)} ={e}^{{log}\left(\sqrt{\mathrm{2}\pi}\right)} =\sqrt{\mathrm{2}\pi} \\ $$ Commented by MJS_new…