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Category: Trigonometry

if-we-have-the-following-system-tanx-tany-a-x-y-we-have-the-general-candition-1-a-1-a-1-sin-1-if-you-apply-the-general-candition-by-the-following-system-it-does-not-give-us-the-real

Question Number 216592 by Davidtim last updated on 11/Feb/25 $${if}\:{we}\:{have}\:{the}\:{following}\:{system}: \\ $$$$\frac{{tanx}}{{tany}}={a} \\ $$$${x}\pm{y}=\alpha \\ $$$${we}\:{have}\:{the}\:{general}\:{candition}: \\ $$$$−\mathrm{1}\leqslant\left(\frac{{a}−\mathrm{1}}{{a}+\mathrm{1}}\right){sin}\alpha\leqslant\mathrm{1} \\ $$$${if}\:{you}\:{apply}\:{the}\:{general}\:{candition}\:{by} \\ $$$${the}\:{following}\:{system}\:{it}\:{does}\:{not}\:{give} \\ $$$${us}\:{the}\:{reality},\:{despite}\:{this}\:{system}\:{have} \\…

Reponse-a-l-exercice-N8-Reponses-par-ordre-1-2-3-4-5-6-imsge-1-imsge-2-image-3-imsge-5-imsge-4-imsge-6-

Question Number 216454 by a.lgnaoui last updated on 08/Feb/25 $$\mathrm{Reponse}\:\mathrm{a}\:\:\mathrm{l}\:\mathrm{exercice}\:\:\mathrm{N8}: \\ $$$$\mathrm{Reponses}\:\mathrm{par}\:\mathrm{ordre}:\left(\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6}\right) \\ $$$$\boldsymbol{\mathrm{imsge}}\:\mathrm{1}\: \\ $$$$\boldsymbol{\mathrm{imsge}}\:\mathrm{2} \\ $$$$\boldsymbol{\mathrm{image}}\:\mathrm{3} \\ $$$$\boldsymbol{\mathrm{imsge}}\:\mathrm{5} \\ $$$$\boldsymbol{\mathrm{imsge}}\:\mathrm{4} \\ $$$$\boldsymbol{\mathrm{imsge}}\:\mathrm{6} \\…

If-asin-bcos-acosec-bsec-then-prove-that-each-term-is-equal-to-a-2-3-b-2-3-a-2-3-b-2-3-

Question Number 216421 by MATHEMATICSAM last updated on 07/Feb/25 $$\mathrm{If}\:{a}\mathrm{sin}\theta\:+\:{b}\mathrm{cos}\theta\:=\:{a}\mathrm{cosec}\theta\:+\:{b}\mathrm{sec}\theta\:\mathrm{then} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{each}\:\mathrm{term}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\left({a}^{\frac{\mathrm{2}}{\mathrm{3}}} \:−\:{b}^{\frac{\mathrm{2}}{\mathrm{3}}} \right)\sqrt{{a}^{\frac{\mathrm{2}}{\mathrm{3}}} \:+\:{b}^{\frac{\mathrm{2}}{\mathrm{3}}} }. \\ $$ Answered by mr W last…

prove-sin-a-b-sin-a-cos-b-sin-b-cos-a-

Question Number 216202 by mahdipoor last updated on 29/Jan/25 $${prove}\::\: \\ $$$${sin}\left({a}+{b}\right)={sin}\left({a}\right){cos}\left({b}\right)+{sin}\left({b}\right){cos}\left({a}\right) \\ $$ Answered by dionigi last updated on 30/Jan/25 $${e}^{{i}\:\left({a}+{b}\right)\:} =\:\mathrm{cos}\left({a}+{b}\right)\:+\:{i}\:\mathrm{sin}\left({a}+{b}\right) \\ $$$${e}^{{i}\:\left({a}+{b}\right)\:}…

Question-215696

Question Number 215696 by BaliramKumar last updated on 15/Jan/25 Answered by MATHEMATICSAM last updated on 15/Jan/25 $$\mathrm{sec}^{\mathrm{4}} \mathrm{x}\:−\:\mathrm{cosec}^{\mathrm{4}} \mathrm{x}\:−\:\mathrm{2sec}^{\mathrm{2}} \mathrm{x}\:+\:\mathrm{2cosec}^{\mathrm{2}} \mathrm{x}\:=\:\frac{\mathrm{63}}{\mathrm{8}} \\ $$$$\Rightarrow\:\mathrm{sec}^{\mathrm{2}} {x}\left(\mathrm{sec}^{\mathrm{2}} {x}\:−\:\mathrm{2}\right)\:+\:\mathrm{cosec}^{\mathrm{2}}…