Question Number 100131 by bemath last updated on 25/Jun/20 $$\mathrm{If}\:\mathrm{3sin}\:\mathrm{x}+\mathrm{4cos}\:\mathrm{x}=\mathrm{5}\:\mathrm{then}\:\mathrm{sin}\:\mathrm{x}=? \\ $$ Commented by bobhans last updated on 25/Jun/20 $$\mathrm{let}\:\mathrm{tan}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)\:=\:\mathrm{t}\:,\:\Rightarrow\mathrm{sin}\:\mathrm{x}\:=\:\frac{\mathrm{2t}}{\mathrm{1}+\mathrm{t}^{\mathrm{2}} }\:,\:\mathrm{cos}\:\mathrm{x}=\frac{\mathrm{1}−\mathrm{t}^{\mathrm{2}} }{\mathrm{1}+\mathrm{t}^{\mathrm{2}} } \\ $$$$\Leftrightarrow\frac{\mathrm{6t}+\mathrm{4}−\mathrm{4t}^{\mathrm{2}}…
Question Number 100130 by bemath last updated on 25/Jun/20 $$\mathrm{how}\:\mathrm{many}\:\mathrm{integer}\:\mathrm{number}\: \\ $$$$\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\frac{\mathrm{sin}\:\mathrm{x}−\mid\mathrm{x}+\mathrm{2}\mid}{\mathrm{x}^{\mathrm{2}} −\mathrm{4x}−\mathrm{5}}\:\geqslant\:\mathrm{0}\: \\ $$ Answered by mr W last updated on 25/Jun/20…
Question Number 165649 by cortano1 last updated on 06/Feb/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 165637 by daus last updated on 05/Feb/22 $$\mathrm{37}{tanx}\:=\mathrm{11}{tan}\mathrm{3}{x} \\ $$$${solve}\:{it} \\ $$ Answered by mr W last updated on 06/Feb/22 $$\mathrm{37}\:\mathrm{tan}\:{x}=\mathrm{11}×\frac{\mathrm{3}\:\mathrm{tan}\:{x}−\mathrm{tan}^{\mathrm{3}} \:{x}}{\mathrm{1}−\mathrm{3}\:\mathrm{tan}^{\mathrm{2}} \:{x}}…
Question Number 165558 by som(math1967) last updated on 03/Feb/22 $${Prove}\:{that} \\ $$$$\:\:\boldsymbol{{sec}}\frac{\mathrm{2}\boldsymbol{\pi}}{\mathrm{7}}\:+\boldsymbol{{sec}}\frac{\mathrm{4}\boldsymbol{\pi}}{\mathrm{7}}+\boldsymbol{{sec}}\frac{\mathrm{8}\boldsymbol{\pi}}{\mathrm{7}}\:=−\mathrm{4} \\ $$ Answered by Rohit143Jo last updated on 04/Feb/22 $${Ans}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{Let},\:{x}=\frac{\mathrm{2}\pi}{\mathrm{7}}\:\:\:\:\Leftrightarrow\:\:\mathrm{7}{x}=\mathrm{2}\pi \\…
Question Number 34420 by math khazana by abdo last updated on 06/May/18 $${let}\:{A}\:\:=\:{arctanx}\:−{arctany} \\ $$$${give}\:{another}\:{form}\:{of}\:{A}\:{if}\:\:{xy}\neq−\mathrm{1}\:. \\ $$ Commented by math khazana by abdo last updated…
Question Number 165428 by mathlove last updated on 01/Feb/22 Answered by som(math1967) last updated on 01/Feb/22 $$\:\frac{{sin}\mathrm{6}{sin}\mathrm{42}{sin}\mathrm{66}{sin}\mathrm{78}}{{cos}\mathrm{6}{cos}\mathrm{42}{cos}\mathrm{66}{cos}\mathrm{78}}\:\:\bigstar \\ $$$$=\frac{\left(\mathrm{2}{sin}\mathrm{6}{sin}\mathrm{66}\right)\left(\mathrm{2}{sin}\mathrm{42}{sin}\mathrm{78}\right)}{\left(\mathrm{2}{cos}\mathrm{6}{cos}\mathrm{66}\right)\left(\mathrm{2}{cos}\mathrm{42}{cos}\mathrm{78}\right)} \\ $$$$=\frac{\left\{{cos}\left(\mathrm{66}−\mathrm{6}\right)−{cos}\left(\mathrm{66}+\mathrm{6}\right)\right\}\left\{{cos}\mathrm{36}−{cos}\mathrm{120}\right\}}{\left({cos}\mathrm{72}+{cos}\mathrm{60}\right)\left({cos}\mathrm{120}+{cos}\mathrm{36}\right)} \\ $$$$=\frac{\left(\frac{\mathrm{1}}{\mathrm{2}}−\frac{\sqrt{\mathrm{5}}−\mathrm{1}}{\mathrm{4}}\right)\left(\frac{\sqrt{\mathrm{5}}+\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{2}}\right)}{\left(\frac{\sqrt{\mathrm{5}}−\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{2}}\right)\left(\frac{\sqrt{\mathrm{5}}+\mathrm{1}}{\mathrm{4}}−\frac{\mathrm{1}}{\mathrm{2}}\right)}\:\:\:\bigstar\bigstar \\ $$$$=\frac{\left(\mathrm{3}−\sqrt{\mathrm{5}}\right)\left(\mathrm{3}+\sqrt{\mathrm{5}}\right)}{\left(\sqrt{\mathrm{5}}+\mathrm{1}\right)\left(\sqrt{\mathrm{5}}−\mathrm{1}\right)}=\frac{\mathrm{9}−\mathrm{5}}{\mathrm{5}−\mathrm{1}}=\mathrm{1}…
Question Number 165382 by mathlove last updated on 31/Jan/22 Commented by mathlove last updated on 01/Feb/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 165370 by daus last updated on 31/Jan/22 Commented by daus last updated on 31/Jan/22 $${solve}\:{x} \\ $$ Answered by Ar Brandon last updated…
Question Number 165314 by mathlove last updated on 29/Jan/22 $$\mathrm{sin}\:^{\mathrm{2}} \mathrm{1}+\mathrm{sin}\:^{\mathrm{2}} \mathrm{2}+\mathrm{sin}\:^{\mathrm{2}} \mathrm{3}+…..+{sin}^{\mathrm{2}} \mathrm{90}=? \\ $$ Commented by cortano1 last updated on 29/Jan/22 $$\mathrm{45}.\mathrm{5}\: \\…