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why-x-0-1-ln-u-x-1-du-I-don-t-know-how-to-prove-this-

Question Number 10555 by paonky last updated on 17/Feb/17 $$\mathrm{why}\:\Gamma\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \left[−\mathrm{ln}\left(\mathrm{u}\right)\right]^{{x}−\mathrm{1}} {du}\:\:? \\ $$$$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{know}\:\mathrm{how}\:\mathrm{to}\:\mathrm{prove}\:\mathrm{this} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question-141627

Question Number 141627 by cherokeesay last updated on 21/May/21 Answered by MJS_new last updated on 21/May/21 $$\frac{\mathrm{sin}\:\mathrm{2}{x}\:+\mathrm{sin}\:\mathrm{4}{x}}{\mathrm{1}+\mathrm{cos}\:\mathrm{2}{x}\:+\mathrm{cos}\:\mathrm{4}{x}}=\frac{−\mathrm{2sin}\:{x}\:\mathrm{cos}\:{x}\:\left(\mathrm{1}−\mathrm{4cos}^{\mathrm{2}} \:{x}\right)}{\mathrm{1}+\mathrm{2cos}^{\mathrm{2}} \:{x}\:\left(\mathrm{1}−\mathrm{4sin}^{\mathrm{2}} \:{x}\right)}= \\ $$$$\:\:\:\:\:\left[\mathrm{sin}\:{x}\:=\frac{\mathrm{tan}\:{x}}{\:\sqrt{\mathrm{1}+\mathrm{tan}^{\mathrm{2}} \:{x}}}\wedge\mathrm{cos}\:{x}\:=\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\mathrm{tan}^{\mathrm{2}} \:{x}}}\right] \\…

what-is-minimal-expression-for-sin-pi-k-cos-pi-k-tan-pi-k-cosec-pi-k-sec-pi-k-and-cot-pi-k-

Question Number 76086 by hejdj last updated on 23/Dec/19 $${what}\:{is}\:{minimal}\:{expression}\:{for}\:\mathrm{sin}\:\frac{\pi}{{k}}\: \\ $$$$\mathrm{cos}\:\frac{\pi}{{k}},\:\mathrm{tan}\:\frac{\pi}{{k}},\:\mathrm{cosec}\:\frac{\pi}{{k}},\mathrm{sec}\:\frac{\pi}{{k}}{and}\:\mathrm{cot}\:\frac{\pi}{{k}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com