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Category: Trigonometry

Question-140746

Question Number 140746 by 676597498 last updated on 12/May/21 Answered by Ar Brandon last updated on 12/May/21 $$\left(\mathrm{i}\right)\:\left(\mathrm{1}+\mathrm{3w}\right)\left(\mathrm{1}+\mathrm{3w}^{\mathrm{2}} \right)=\mathrm{1}+\mathrm{3}\left(\mathrm{w}^{\mathrm{2}} +\mathrm{w}\right)+\mathrm{9w}^{\mathrm{3}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{1}+\mathrm{3}\left(−\mathrm{w}^{\mathrm{3}} \right)+\mathrm{9}\left(\mathrm{1}\right)=\mathrm{1}−\mathrm{3}+\mathrm{9}=\mathrm{7} \\ $$$$…

Prove-that-cos-18-0-sin-18-0-2-sin-2-

Question Number 75208 by vishalbhardwaj last updated on 08/Dec/19 $$\:\mathrm{Prove}\:\mathrm{that}\::\:\mathrm{cos}\:\mathrm{18}^{\mathrm{0}} −\mathrm{sin}\:\mathrm{18}^{\mathrm{0}} \:=\:\sqrt{\mathrm{2}}\:\mathrm{sin}\:\mathrm{2} \\ $$ Answered by Kunal12588 last updated on 08/Dec/19 $${cos}\:\mathrm{18}°−{sin}\mathrm{18}° \\ $$$$=\sqrt{\mathrm{2}}{sin}\left(\mathrm{45}°−\mathrm{18}°\right) \\…

Question-75209

Question Number 75209 by vishalbhardwaj last updated on 08/Dec/19 Answered by Kunal12588 last updated on 08/Dec/19 $${x}+{y}+{z}={xyz} \\ $$$${let}\:{x}={tan}\:\alpha,{y}={tan}\:\beta,\:{z}={tan}\:\gamma \\ $$$${tan}\:\alpha\:+\:{tan}\:\beta\:+\:{tan}\:\gamma\:=\:{tan}\:\alpha\:{tan}\:\beta\:{tan}\:\gamma \\ $$$$\Rightarrow{tan}\:\gamma\:\left(\mathrm{1}−{tan}\:\alpha\:{tan}\:\beta\right)=−\left({tan}\:\alpha+{tan}\:\beta\right) \\ $$$$\Rightarrow{tan}\:\gamma=−\frac{{tan}\:\alpha+{tan}\beta}{\mathrm{1}−{tan}\:\alpha\:{tan}\:\beta}=−{tan}\:\left(\alpha+\beta\right)…

hello-show-that-sin-5pi-18-cos-13pi-18-1-2-sin-4pi-9-

Question Number 75147 by mathocean1 last updated on 07/Dec/19 $$\mathrm{hello} \\ $$$$\mathrm{show}\:\mathrm{that}\: \\ $$$$\mathrm{sin}\frac{\mathrm{5}\pi}{\mathrm{18}}\mathrm{cos}\frac{\mathrm{13}\pi}{\mathrm{18}}=−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}\frac{\mathrm{4}\pi}{\mathrm{9}} \\ $$ Answered by MJS last updated on 07/Dec/19 $$\mathrm{sin}\:{a}\:\mathrm{cos}\:{b}\:=\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{sin}\:\left({a}−{b}\right)\:+\mathrm{sin}\:\left({a}+{b}\right)\right) \\…

please-help-me-to-show-that-tan-2-pi-8-2tan-pi-8-1-0-

Question Number 75131 by mathocean1 last updated on 07/Dec/19 $$\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{to}\:\mathrm{show}\:\mathrm{that} \\ $$$$\mathrm{tan}^{\mathrm{2}} \left(\frac{\pi}{\mathrm{8}}\right)+\mathrm{2tan}\left(\frac{\pi}{\mathrm{8}}\right)−\mathrm{1}=\mathrm{0} \\ $$ Answered by mr W last updated on 07/Dec/19 $$\mathrm{tan}\:\frac{\pi}{\mathrm{4}}=\mathrm{1} \\…

Eliminate-from-the-equation-x-a-cos-y-b-sin-cos-2-x-a-sin-y-b-cos-2sin-2-

Question Number 140659 by bemath last updated on 11/May/21 $$\mathrm{Eliminate}\:\theta\:\mathrm{from}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\:\begin{cases}{\frac{\mathrm{x}}{\mathrm{a}}\mathrm{cos}\:\theta−\frac{\mathrm{y}}{\mathrm{b}}\mathrm{sin}\:\theta=\mathrm{cos}\:\mathrm{2}\theta}\\{\frac{\mathrm{x}}{\mathrm{a}}\mathrm{sin}\:\theta+\frac{\mathrm{y}}{\mathrm{b}}\mathrm{cos}\:\theta=\mathrm{2sin}\:\mathrm{2}\theta}\end{cases} \\ $$ Answered by BHOOPENDRA last updated on 11/May/21 Answered by BHOOPENDRA last…

If-x-1-x-2-x-3-x-2009-R-Find-the-minimum-value-from-cos-x-1-sin-x-2-cos-x-2-sin-x-3-cos-x-2008-sin-x-2009-cos-x-2009-sin-x-1-

Question Number 9525 by Joel575 last updated on 12/Dec/16 $$\mathrm{If}\:{x}_{\mathrm{1}} ,\:{x}_{\mathrm{2}} ,\:{x}_{\mathrm{3}} ,\:…,\:{x}_{\mathrm{2009}\:} \in\:\mathbb{R} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{from} \\ $$$$\left(\mathrm{cos}\:{x}_{\mathrm{1}} \right)\left(\mathrm{sin}\:{x}_{\mathrm{2}} \right)\:+\:\left(\mathrm{cos}\:{x}_{\mathrm{2}} \right)\left(\mathrm{sin}\:{x}_{\mathrm{3}} \right)\:+\:…\:+\:\left(\mathrm{cos}\:{x}_{\mathrm{2008}} \right)\left(\mathrm{sin}\:{x}_{\mathrm{2009}} \right)\:+\:\left(\mathrm{cos}\:{x}_{\mathrm{2009}} \right)\left(\mathrm{sin}\:{x}_{\mathrm{1}}…