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Category: Trigonometry

Given-sin-1-sin-a-sin-b-sin-1-sin-a-sin-b-pi-2-what-is-the-value-of-sin-2-a-sin-2-b-

Question Number 130082 by benjo_mathlover last updated on 22/Jan/21 $$\mathrm{Given}\:\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{sin}\:{a}+\mathrm{sin}\:{b}\right)+\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{sin}\:{a}−\mathrm{sin}\:{b}\right)=\frac{\pi}{\mathrm{2}} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{sin}\:^{\mathrm{2}} {a}\:+\mathrm{sin}\:^{\mathrm{2}} {b}. \\ $$ Answered by liberty last updated on 22/Jan/21…

The-maximum-value-of-f-x-sin-2-2pi-3-x-sin-2-2pi-3-x-is-

Question Number 130054 by EDWIN88 last updated on 22/Jan/21 $$\mathrm{The}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{sin}\:^{\mathrm{2}} \left(\frac{\mathrm{2}\pi}{\mathrm{3}}+\mathrm{x}\right)+\mathrm{sin}\:^{\mathrm{2}} \left(\frac{\mathrm{2}\pi}{\mathrm{3}}−\mathrm{x}\right)\:\mathrm{is}\:? \\ $$ Answered by liberty last updated on 22/Jan/21 Commented by MJS_new last…

Given-4cos-2-x-sin-x-2sin-2-x-3sin-x-where-pi-2-x-pi-2-Find-the-sum-of-all-posibble-value-of-x-

Question Number 130047 by liberty last updated on 22/Jan/21 $$\:\mathrm{Given}\:\mathrm{4cos}\:^{\mathrm{2}} \mathrm{x}\:\mathrm{sin}\:\mathrm{x}−\mathrm{2sin}\:^{\mathrm{2}} \mathrm{x}\:=\:\mathrm{3sin}\:\mathrm{x} \\ $$$$\mathrm{where}\:−\frac{\pi}{\mathrm{2}}\leqslant\mathrm{x}\leqslant\frac{\pi}{\mathrm{2}}\:.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of} \\ $$$$\mathrm{all}\:\mathrm{posibble}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}. \\ $$ Answered by MJS_new last updated on 22/Jan/21…

Given-A-and-B-are-the-solution-of-equation-a-tan-x-b-sec-x-c-find-tan-A-B-

Question Number 130041 by liberty last updated on 22/Jan/21 $$\mathrm{Given}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{are}\:\mathrm{the}\:\mathrm{solution} \\ $$$$\mathrm{of}\:\mathrm{equation}\:{a}\:\mathrm{tan}\:{x}\:+\:{b}\:\mathrm{sec}\:{x}\:=\:{c}\: \\ $$$${find}\:\mathrm{tan}\:\left({A}+\mathrm{B}\right). \\ $$ Answered by nueron last updated on 22/Jan/21 Commented by…

please-anyone-help-me-to-solve-this-i-k-1-n-cos-k-2-pi-n-ii-k-1-n-sin-k-2-pi-n-thank-you-

Question Number 64498 by slotto last updated on 18/Jul/19 $$\mathrm{please},\:\mathrm{anyone}\:\mathrm{help}\:\mathrm{me}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{this} \\ $$$$\mathrm{i}.\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{cos}\left(\frac{\mathrm{k}^{\mathrm{2}} \pi}{\mathrm{n}}\right) \\ $$$$\mathrm{ii}.\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\Sigma}}\mathrm{sin}\left(\frac{\mathrm{k}^{\mathrm{2}} \pi}{\mathrm{n}}\right) \\ $$$$\mathrm{thank}\:\mathrm{you}. \\ $$ Terms…

8-1-sin-pi-8-1-sin-3pi-8-1-sin-5pi-8-1-sin-7pi-8-

Question Number 129807 by bramlexs22 last updated on 19/Jan/21 $$\:\mathrm{8}.\left(\mathrm{1}+\mathrm{sin}\:\frac{\pi}{\mathrm{8}}\right)\left(\mathrm{1}+\mathrm{sin}\frac{\mathrm{3}\pi}{\mathrm{8}}\right)\left(\mathrm{1}−\mathrm{sin}\:\frac{\mathrm{5}\pi}{\mathrm{8}}\right)\left(\mathrm{1}−\mathrm{sin}\:\frac{\mathrm{7}\pi}{\mathrm{8}}\right)=?\: \\ $$ Answered by EDWIN88 last updated on 19/Jan/21 $$\:\mathrm{sin}\:\mathrm{x}\:=\:\mathrm{sin}\:\left(\pi−\mathrm{x}\right) \\ $$$$\:\mathrm{sin}\:\frac{\mathrm{3}\pi}{\mathrm{8}}=\mathrm{sin}\:\frac{\mathrm{5}\pi}{\mathrm{8}}\:\mathrm{and}\:\mathrm{sin}\:\frac{\mathrm{7}\pi}{\mathrm{8}}=\mathrm{sin}\:\frac{\pi}{\mathrm{8}} \\ $$$$\Leftrightarrow\:\mathrm{8}\left(\mathrm{1}+\mathrm{sin}\:\frac{\pi}{\mathrm{8}}\right)\left(\mathrm{1}−\mathrm{sin}\:\frac{\pi}{\:\mathrm{8}}\right)\left(\mathrm{1}+\mathrm{sin}\:\frac{\mathrm{3}\pi}{\mathrm{8}}\right)\left(\mathrm{1}−\mathrm{sin}\:\frac{\mathrm{3}\pi}{\mathrm{8}}\right)= \\…

cot-15-cot-16-cot-17-cot-75-

Question Number 129801 by bramlexs22 last updated on 19/Jan/21 $$\:\mathrm{cot}\:\mathrm{15}°\:\mathrm{cot}\:\mathrm{16}°\:\mathrm{cot}\:\mathrm{17}°…\:\mathrm{cot}\:\mathrm{75}°= \\ $$ Answered by EDWIN88 last updated on 19/Jan/21 $$=\mathrm{1} \\ $$$$\:\left[\:\mathrm{cot}\:\mathrm{15}°=\mathrm{tan}\:\mathrm{75}°\:\mathrm{etc}\:\right]\: \\ $$ Terms…

cos-pisin-x-3-sin-picos-x-3-x-

Question Number 129719 by bramlexs22 last updated on 18/Jan/21 $$\:\:\mathrm{cos}\:\left(\pi\mathrm{sin}\:\left(\frac{\mathrm{x}}{\mathrm{3}}\right)\right)=\mathrm{sin}\:\left(\pi\mathrm{cos}\:\left(\frac{\mathrm{x}}{\mathrm{3}}\right)\right) \\ $$$$\:\:\mathrm{x}\:=? \\ $$$$ \\ $$ Answered by liberty last updated on 18/Jan/21 $$\:\mathrm{cos}\:\left(\pi\mathrm{sin}\:\frac{\mathrm{x}}{\mathrm{3}}\right)=\mathrm{cos}\:\left(\frac{\pi}{\mathrm{2}}−\pi\mathrm{cos}\:\frac{\mathrm{x}}{\mathrm{3}}\right) \\…