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Author: Tinku Tara

Question-17676

Question Number 17676 by mondodotto@gmail.com last updated on 09/Jul/17 Answered by alex041103 last updated on 09/Jul/17 $$\mathrm{First}: \\ $$$$\frac{\mathrm{5cos}^{\mathrm{3}} \mathrm{x}\:+\:\mathrm{2sin}^{\mathrm{3}} \mathrm{x}}{\mathrm{2sin}^{\mathrm{2}} \mathrm{xcos}^{\mathrm{2}} \mathrm{x}}\:=\:\frac{\mathrm{5}}{\mathrm{2}}\:\frac{\mathrm{cosx}}{\mathrm{sin}^{\mathrm{2}} \mathrm{x}}+\frac{\mathrm{sinx}}{\mathrm{cos}^{\mathrm{2}} \mathrm{x}}…

Question-17675

Question Number 17675 by mondodotto@gmail.com last updated on 09/Jul/17 Answered by Tinkutara last updated on 10/Jul/17 $$\mathrm{Let}\:{a}^{{y}} \:=\:{x}\:\left(\boldsymbol{{i}}\right) \\ $$$$\mathrm{Taking}\:\mathrm{log}\:\mathrm{on}\:\mathrm{both}\:\mathrm{sides},\:\mathrm{log}_{{a}} \:{x}\:=\:{y} \\ $$$$\mathrm{Substituting}\:\mathrm{this}\:\mathrm{value}\:\mathrm{of}\:{y}\:\mathrm{in}\:\left(\boldsymbol{{i}}\right),\:\mathrm{we} \\ $$$$\mathrm{get}\:\boldsymbol{{a}}^{\boldsymbol{\mathrm{log}}_{\boldsymbol{{a}}}…

Prove-that-x-pi-4-n-0-cos-x-2-n-cos-pi-2x-2-n-1-2-4cos2x-pi-pi-4x-

Question Number 83209 by ~blr237~ last updated on 28/Feb/20 $$\:\:\:{Prove}\:{that}\:\:\forall\:\:{x}\neq\frac{\pi}{\mathrm{4}}\:\:\:,\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\prod}}\left(\frac{{cos}\left(\frac{{x}}{\mathrm{2}^{{n}} }\right)+{cos}\left(\frac{\pi−\mathrm{2}{x}}{\mathrm{2}^{{n}+\mathrm{1}} }\right)}{\mathrm{2}}\:\right)\:=\:\frac{\mathrm{4}{cos}\mathrm{2}{x}}{\pi\left(\pi−\mathrm{4}{x}\right)}\: \\ $$ Answered by mind is power last updated on 28/Feb/20…

1-find-0-pi-4-dx-2-a-sinx-areal-2-c-explicite-0-pi-4-sinx-2-asinx-2-dx-

Question Number 83206 by mathmax by abdo last updated on 28/Feb/20 $$\left.\mathrm{1}\right)\:{find}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\frac{{dx}}{\mathrm{2}+{a}\:{sinx}}\:\:\:\:\left({areal}\right) \\ $$$$\left.\mathrm{2}\right)\:{c}\:{explicite}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\frac{{sinx}}{\left(\mathrm{2}+{asinx}\right)^{\mathrm{2}} }{dx} \\ $$ Commented by mathmax by…

t-1-t-ln-x-dx-

Question Number 83204 by M±th+et£s last updated on 28/Feb/20 $$\int_{{t}−\mathrm{1}} ^{{t}} {ln}\left({x}!\right){dx}=? \\ $$ Commented by MJS last updated on 28/Feb/20 $$\mathrm{if}\:\mathrm{you}\:\mathrm{use}\:{x}!\:\mathrm{it}'\mathrm{s}\:\mathrm{only}\:\mathrm{defined}\:\mathrm{for}\:{x}\in\mathbb{N}\:\Rightarrow\:\mathrm{no} \\ $$$$\mathrm{integral}\:\mathrm{possible} \\…