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Category: Trigonometry

Q-1-1-cos-2-2A-2-cos-4-A-sin-4-A-2-sin-2-A-sin-2-120-0-A-sin-2-120-0-A-3-2-

Question Number 8401 by rhm last updated on 10/Oct/16 $${Q}\:.\mathrm{1}\:\:\:\mathrm{1}+{cos}^{\mathrm{2}} \mathrm{2}{A}=\mathrm{2}\left({cos}^{\mathrm{4}} \:{A}+{sin}^{\mathrm{4}} \:{A}\right) \\ $$$$\mathrm{2}.\:\:{sin}^{\mathrm{2}} {A}+{sin}^{\mathrm{2}} \left(\mathrm{120}^{\mathrm{0}} +{A}\right)+{sin}^{\mathrm{2}} \left(\mathrm{120}^{\mathrm{0}} −{A}\right) \\ $$$$=\:\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$ \\…

hi-prove-this-cos-pi-10-cos-4pi-10-cos-6pi-10-cos-9pi-10-0-by-the-easiest-possible-way-

Question Number 139409 by henderson last updated on 26/Apr/21 $$\mathrm{hi}\:! \\ $$$$\mathrm{prove}\:\mathrm{this}\::\: \\ $$$${cos}\:\frac{\pi}{\mathrm{10}}\:+\:{cos}\:\frac{\mathrm{4}\pi}{\mathrm{10}}\:+\:{cos}\:\frac{\mathrm{6}\pi}{\mathrm{10}}\:+\:{cos}\:\frac{\mathrm{9}\pi}{\mathrm{10}}\:=\:\mathrm{0}. \\ $$$$\left(\mathrm{by}\:\mathrm{the}\:\mathrm{easiest}\:\mathrm{possible}\:\mathrm{way}…!\right) \\ $$ Answered by mr W last updated on…

Solve-the-equation-6cos2a-5sin2a-1-8-for0-a-180-

Question Number 8311 by lepan last updated on 07/Oct/16 $${Solve}\:{the}\:{equation}\:\mathrm{6}{cos}\mathrm{2}{a}−\mathrm{5}{sin}\mathrm{2}{a}=\mathrm{1}.\mathrm{8} \\ $$$${for}\mathrm{0}°\leqslant{a}\leqslant\mathrm{180}°. \\ $$ Commented by 123456 last updated on 07/Oct/16 $$\mathrm{6cos2}{a}−\mathrm{5sin2}{a}=\mathrm{1}.\mathrm{8} \\ $$$$\mathrm{cos}^{\mathrm{2}} \mathrm{2}{a}+\mathrm{sin}^{\mathrm{2}}…

Question-8314

Question Number 8314 by tawakalitu last updated on 07/Oct/16 Commented by Tinku Tara last updated on 08/Oct/16 $$\mathrm{For}\:\mathrm{othercases}\:\mathrm{can}\:\mathrm{u}\:\mathrm{please}\:\mathrm{email} \\ $$$$\mathrm{picture}\:\mathrm{to}\:\mathrm{us}\:\mathrm{at}\:\mathrm{infoattinkutara}.\mathrm{com} \\ $$$$\mathrm{and}\:\mathrm{we}\:\mathrm{will}\:\mathrm{troubleshoot}\:\mathrm{the}\:\mathrm{issue}. \\ $$$$\mathrm{Alternatively}\:\mathrm{try}\:\mathrm{to}\:\mathrm{post}\:\mathrm{image}\:\mathrm{as}\:\mathrm{a}\:\mathrm{new} \\…

If-270-lt-x-lt-360-simplify-2-2-2cosx-

Question Number 8306 by lepan last updated on 07/Oct/16 $${If}\:\mathrm{270}°<{x}<\mathrm{360}°,\:{simplify} \\ $$$$\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\mathrm{2}{cosx}}}. \\ $$ Commented by sou1618 last updated on 07/Oct/16 $$\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\mathrm{2}{cosx}}}\:\left(\mathrm{270}°<{x}<\mathrm{360}°\right) \\ $$$$\mathrm{2}{cos}^{\mathrm{2}} \alpha=\mathrm{1}+{cos}\mathrm{2}\alpha…

B-y-expessing-each-side-of-the-equation-in-terms-of-tanA-or-otherwise-show-that-sin2A-cos2A-1-sin2A-cos2A-1-tan-45-A-tanA-

Question Number 8297 by lepan last updated on 06/Oct/16 $$\underset{} {{B}y}\:{expessing}\:{each}\:{side}\:{of}\:{the} \\ $$$${equation}\:{in}\:{terms}\:{of}\:{tanA}\:,{or}\: \\ $$$${otherwise}\:{show}\:{that} \\ $$$$\frac{{sin}\mathrm{2}{A}+{cos}\mathrm{2}{A}+\mathrm{1}}{{sin}\mathrm{2}{A}+{cos}\mathrm{2}{A}−\mathrm{1}}=\frac{{tan}\left(\mathrm{45}°+{A}\right)}{{tanA}} \\ $$ Answered by Rasheed Soomro last updated…

Show-that-tan-tan-tan-1-tan-tan-

Question Number 8287 by lepan last updated on 06/Oct/16 $${Show}\:{that}\:{tan}\left(\alpha+\beta\right)=\frac{{tan}\alpha+{tan}\beta}{\mathrm{1}−{tan}\alpha{tan}\beta}. \\ $$ Answered by ridwan balatif last updated on 06/Oct/16 $$\mathrm{tan}\left(\alpha+\beta\right)=\frac{\mathrm{sin}\left(\alpha+\beta\right)}{\mathrm{cos}\left(\alpha+\beta\right)} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{sin}\alpha\mathrm{cos}\beta+\mathrm{sin}\beta\mathrm{cos}\alpha}{\mathrm{cos}\alpha\mathrm{cos}\beta−\mathrm{sin}\alpha\mathrm{sin}\beta} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\left(\mathrm{sin}\alpha\mathrm{cos}\beta+\mathrm{sin}\beta\mathrm{cos}\alpha\right).\left(\frac{\mathrm{1}}{\mathrm{cos}\alpha\mathrm{cos}\beta}\right)}{\left(\mathrm{cos}\alpha\mathrm{cos}\beta−\mathrm{sin}\alpha\mathrm{sin}\beta\right).\left(\frac{\mathrm{1}}{\mathrm{cos}\alpha\mathrm{cos}\beta}\right)}…