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Author: Tinku Tara

Suppose-that-sec-x-tan-x-22-7-cosec-x-cot-x-m-n-m-n-is-in-the-lowest-term-Find-m-n-

Question Number 149598 by naka3546 last updated on 06/Aug/21 $${Suppose}\:\:{that}\:\: \\ $$$$\mathrm{sec}\:{x}\:+\:\mathrm{tan}\:{x}\:=\:\frac{\mathrm{22}}{\mathrm{7}} \\ $$$$\mathrm{cosec}\:{x}\:+\:\mathrm{cot}\:{x}\:=\:\frac{{m}}{{n}} \\ $$$$\frac{{m}}{{n}}\:\:{is}\:\:{in}\:\:{the}\:\:{lowest}\:\:{term}\:. \\ $$$${Find}\:\:{m}\:+\:{n}\:. \\ $$ Answered by iloveisrael last updated…

The-number-of-solutions-of-the-equation-sin-3-x-3sinxcos-2-x-2cos-3-x-0-in-pi-4-pi-4-is-

Question Number 18524 by Tinkutara last updated on 23/Jul/17 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solutions}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{sin}^{\mathrm{3}} {x}\:−\:\mathrm{3sin}{x}\mathrm{cos}^{\mathrm{2}} {x}\:+\:\mathrm{2cos}^{\mathrm{3}} {x}\:=\:\mathrm{0}\:\mathrm{in} \\ $$$$\left[−\frac{\pi}{\mathrm{4}},\:\frac{\pi}{\mathrm{4}}\right]\:\mathrm{is} \\ $$ Answered by Tinkutara last updated on…

Match-the-following-Column-I-Trigonometric-equation-A-sin-9-cos-pi-2-B-sin-5-sin-pi-2-2-C-cos-11-cos-3-D-3-tan-15-tan-15-Column-II-Family-of-solutions

Question Number 18523 by Tinkutara last updated on 23/Jul/17 $$\mathrm{Match}\:\mathrm{the}\:\mathrm{following} \\ $$$$\boldsymbol{\mathrm{Column}}-\boldsymbol{\mathrm{I}}\:\left(\boldsymbol{\mathrm{Trigonometric}}\:\boldsymbol{\mathrm{equation}}\right) \\ $$$$\left(\mathrm{A}\right)\:\mathrm{sin}\:\mathrm{9}\theta\:=\:\mathrm{cos}\:\left(\frac{\pi}{\mathrm{2}}\:−\:\theta\right) \\ $$$$\left(\mathrm{B}\right)\:\mathrm{sin}\:\mathrm{5}\theta\:=\:\mathrm{sin}\:\left(\frac{\pi}{\mathrm{2}}\:+\:\mathrm{2}\theta\right) \\ $$$$\left(\mathrm{C}\right)\:\mathrm{cos}\:\mathrm{11}\theta\:=\:\mathrm{cos}\:\mathrm{3}\theta \\ $$$$\left(\mathrm{D}\right)\:\mathrm{3}\:\mathrm{tan}\:\left(\theta\:−\:\mathrm{15}°\right)\:=\:\mathrm{tan}\:\left(\theta\:+\:\mathrm{15}°\right) \\ $$$$\boldsymbol{\mathrm{Column}}-\boldsymbol{\mathrm{II}}\:\left(\boldsymbol{\mathrm{Family}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{solutions}}\right) \\ $$$$\left(\mathrm{p}\right)\:\left(\mathrm{2}{n}\:+\:\mathrm{1}\right)\frac{\pi}{\mathrm{10}},\:{n}\:\in\:{Z} \\…

Find-dy-dx-of-x-m-x-n-x-y-m-n-

Question Number 84059 by niroj last updated on 09/Mar/20 $$ \\ $$$$\:\boldsymbol{\mathrm{Find}}\:\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}\:\boldsymbol{\mathrm{of}}\:\:\:\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{m}}} \boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{n}}} \:=\left(\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}\right)^{\boldsymbol{\mathrm{m}}+\boldsymbol{\mathrm{n}}} . \\ $$ Commented by jagoll last updated on 09/Mar/20 $${x}^{{m}+{n}}…

x-1-y-2-y-1-z-2-z-1-x-2-x-y-z-

Question Number 149588 by mathdanisur last updated on 06/Aug/21 $$\begin{cases}{{x}\:+\:\frac{\mathrm{1}}{{y}}\:=\:\mathrm{2}}\\{{y}\:+\:\frac{\mathrm{1}}{{z}}\:=\:\mathrm{2}}\\{{z}\:+\:\frac{\mathrm{1}}{{x}}\:=\:\mathrm{2}}\end{cases}\:\:\:\Rightarrow\:\:{x};{y};{z}=? \\ $$ Commented by Ar Brandon last updated on 06/Aug/21 $$\mathrm{1};\mathrm{1};\mathrm{1} \\ $$ Commented by…

0-2-x-2-3x-x-2-dx-

Question Number 84055 by naka3546 last updated on 09/Mar/20 $$\underset{\:\mathrm{0}} {\int}\overset{\:\mathrm{2}} {\:}\:\:\frac{{x}^{\mathrm{2}} +\mathrm{3}{x}}{\:\sqrt{{x}+\mathrm{2}}}\:\:{dx}\:\:=\:\:? \\ $$ Commented by mathmax by abdo last updated on 09/Mar/20 $${A}\:=\int_{\mathrm{0}}…

if-x-y-z-gt-0-and-x-2-y-2-z-2-3-then-x-2-y-2-2x-2-y-2-y-2-2x-2-2-3-

Question Number 149585 by mathdanisur last updated on 06/Aug/21 $${if}\:\:{x};{y};{z}>\mathrm{0}\:\:{and}\:\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} =\mathrm{3}\:\:{then}: \\ $$$$\Sigma\:\frac{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }{\left(\mathrm{2}{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)\left({y}^{\mathrm{2}} +\mathrm{2}{x}^{\mathrm{2}} \right)}\:\geqslant\:\frac{\mathrm{2}}{\mathrm{3}} \\ $$ Answered by…

log-x-1-6x-1-1-8-log-3-x-2-3-log-3-x-log-3-x-2-1-0-

Question Number 84051 by john santu last updated on 09/Mar/20 $$\frac{\mathrm{log}_{\left({x}−\mathrm{1}\right)} \:\left(\mathrm{6}{x}−\mathrm{1}\right)}{\left(\frac{\mathrm{1}}{\mathrm{8}}\left(\mathrm{log}_{\mathrm{3}} \left({x}^{\mathrm{2}} \right)\right)^{\mathrm{3}} −\mathrm{log}_{\mathrm{3}} \:\left({x}\right)\right)\left(\mathrm{log}_{\mathrm{3}} \:\left({x}−\mathrm{2}\right)−\mathrm{1}\right)}\:\geqslant\:\mathrm{0} \\ $$ Answered by john santu last updated…