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Author: Tinku Tara

prove-that-sin-x-cos-2x-1-4sin-4x-sec-x-

Question Number 85623 by jagoll last updated on 23/Mar/20 $$\mathrm{prove}\:\mathrm{that}\: \\ $$$$\mathrm{sin}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{2x}\:=\:\frac{\mathrm{1}}{\mathrm{4sin}\:\mathrm{4x}\:\mathrm{sec}\:\mathrm{x}} \\ $$ Answered by Henri Boucatchou last updated on 23/Mar/20 $${Wrong}\:{Sir}; \\ $$$${Take}\:\:{x}=\frac{\pi}{\mathrm{4}},\:\:\mathrm{0}\neq\frac{\mathrm{1}}{\mathrm{0}}…

Question-151144

Question Number 151144 by mnjuly1970 last updated on 18/Aug/21 Answered by qaz last updated on 18/Aug/21 $$\frac{\mathrm{1}}{\mathrm{n}}\int_{−\infty} ^{+\infty} \frac{\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{e}^{\mathrm{x}} \right)}{\mathrm{cosh}\:\left(\frac{\mathrm{x}}{\mathrm{n}}\right)}\mathrm{dx} \\ $$$$=\int_{−\infty} ^{+\infty} \frac{\mathrm{tan}^{−\mathrm{1}}…

Question-85606

Question Number 85606 by Rio Michael last updated on 23/Mar/20 Commented by Rio Michael last updated on 23/Mar/20 $$\mathrm{given}\:\mathrm{that}\:\mathrm{three}\:\mathrm{weights}\:\mathrm{W}_{\mathrm{1}} ,\:\mathrm{W}_{\mathrm{2}} \:{and}\:\mathrm{5}{N}\:\mathrm{are}\:\mathrm{suspended}\:\mathrm{as}\:\mathrm{shown}\:\mathrm{above}. \\ $$$$\mathrm{A}\:\mathrm{light}\:\mathrm{inextensible}\:\mathrm{string}\:\mathrm{passing}\:\mathrm{over}\:\mathrm{smooth}\:\mathrm{fixed}\:\mathrm{pulleys}\:\:\mathrm{makes}\:\mathrm{angles} \\ $$$$\mathrm{40}°\:\mathrm{and}\:\mathrm{60}°\:\mathrm{with}\:\mathrm{the}\:\mathrm{vertical}\:\mathrm{and}\:\mathrm{all}\:\mathrm{the}\:\mathrm{stings}\:\mathrm{are}\:\mathrm{taunt}\:\mathrm{at}\:\mathrm{point}\:\mathrm{A}.…

if-x-y-z-R-and-1-x-2-1-y-2-1-z-2-27-4-prove-that-x-3-y-2-x-2-y-2-y-3-z-2-y-2-z-2-z-3-x-2-z-2-x-2-5-2-

Question Number 151142 by mathdanisur last updated on 18/Aug/21 $$\mathrm{if}\:\:\mathrm{x};\mathrm{y};\mathrm{z}\in\mathbb{R}^{+} \:\:\mathrm{and}\:\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{y}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{z}^{\mathrm{2}} }\:=\:\frac{\mathrm{27}}{\mathrm{4}} \\ $$$$\mathrm{prove}\:\mathrm{that}: \\ $$$$\frac{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} }\:+\:\frac{\mathrm{y}^{\mathrm{3}} \:+\:\mathrm{z}^{\mathrm{2}} }{\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{z}^{\mathrm{2}}…

prove-the-relation-0-1-li-5-x-1-5-x-1-5-dx-5-4-25-3072-2-2-6-3-2-4-4-2-2-5-

Question Number 85603 by M±th+et£s last updated on 23/Mar/20 $${prove}\:{the}\:{relation} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{li}_{\mathrm{5}} \left(\sqrt[{\mathrm{5}}]{{x}}\right)}{\:\sqrt[{\mathrm{5}}]{{x}}}{dx}=\frac{\mathrm{5}}{\mathrm{4}}\left(\frac{\mathrm{25}}{\mathrm{3072}}−\frac{\zeta\left(\mathrm{2}\right)}{\mathrm{2}^{\mathrm{6}} }+\frac{\zeta\left(\mathrm{3}\right)}{\mathrm{2}^{\mathrm{4}} }−\frac{\zeta\left(\mathrm{4}\right)}{\mathrm{2}^{\mathrm{2}} }+\zeta\left(\mathrm{5}\right)\right) \\ $$ Terms of Service Privacy Policy…