Question Number 30087 by rahul 19 last updated on 16/Feb/18 $$\mathrm{solve}: \\ $$$$\mathrm{cos3}{x}.{cos}^{\mathrm{3}} {x}+\mathrm{sin}\:\mathrm{3}{x}.\mathrm{sin}\:^{\mathrm{3}} {x}=\mathrm{0}. \\ $$ Answered by MJS last updated on 16/Feb/18 $${x}=\frac{\pi}{\mathrm{4}}+\frac{\pi\centerdot{z}}{\mathrm{2}};\:{z}\in\mathbb{Z}…
Question Number 30054 by rahul 19 last updated on 15/Feb/18 Answered by ajfour last updated on 16/Feb/18 $${let}\:\:\mathrm{sin}\:{x}=\:{s} \\ $$$$\mathrm{5}{s}^{\mathrm{2}} +\mathrm{4}{s}^{\mathrm{2}} \left(\mathrm{1}−{s}^{\mathrm{2}} \right)−\mathrm{4}\left(\mathrm{1}−\mathrm{2}{s}^{\mathrm{2}} \right)\:>\:\mathrm{0} \\…
Question Number 30000 by ajfour last updated on 14/Feb/18 $${If}\:\mathrm{cos}\:\alpha\:=\:\mathrm{sin}\:\beta\:\mathrm{sin}\:\phi=\mathrm{sin}\:\gamma\:\mathrm{cos}\:\psi \\ $$$$\:\:\:\:\:\:\mathrm{cos}\:\beta\:=\:\mathrm{sin}\:\gamma\:\mathrm{sin}\:\psi\:=\mathrm{sin}\:\alpha\:\mathrm{cos}\:\theta \\ $$$$\:\:\:\:\:\:\mathrm{cos}\:\gamma\:=\:\mathrm{sin}\:\alpha\:\mathrm{sin}\:\theta\:=\mathrm{sin}\:\beta\:\mathrm{cos}\:\phi \\ $$$${then}\:{find}\:\:\mathrm{cos}\:\alpha,\:\mathrm{cos}\:\beta\:,\:\mathrm{cos}\:\gamma\:\:\: \\ $$$${briefly}\:{and}\:{if}\:{possible}\:{linearly} \\ $$$${in}\:{terms}\:{of}\:{only}\:\mathrm{sin}\:\theta,\:\mathrm{cos}\:\theta, \\ $$$$\mathrm{sin}\:\phi,\:\mathrm{cos}\:\phi,\:\mathrm{sin}\:\psi,\:\mathrm{cos}\:\psi\:. \\ $$ Commented…
Question Number 95531 by Abdulrahman last updated on 25/May/20 $$\frac{\mathrm{tanx}×\mathrm{ctg2x}}{\mathrm{tan}^{\mathrm{2}} \mathrm{x}−\mathrm{1}}=? \\ $$ Commented by PRITHWISH SEN 2 last updated on 25/May/20 $$\mathrm{put}\:\mathrm{cot2x}\:=\:\frac{\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}}{\mathrm{2tan}\:\mathrm{x}} \\…
Question Number 161060 by pete last updated on 11/Dec/21 $$\mathrm{Given}\:\mathrm{sin}\left(\mathrm{5x}−\mathrm{38}\right)=\mathrm{cos}\left(\mathrm{2x}+\mathrm{16}\right),\:\mathrm{0}°\leqslant\mathrm{x}\leqslant\mathrm{90}°, \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x} \\ $$ Commented by cortano last updated on 11/Dec/21 $$\:{recall}\:\mathrm{sin}\:\left(\mathrm{90}°−{x}\right)=\:\mathrm{cos}\:{x} \\ $$$$\Leftrightarrow\:\mathrm{sin}\:\left(\mathrm{5}{x}−\mathrm{38}°\right)=\:\mathrm{sin}\:\left(\mathrm{90}°−\left(\mathrm{128}°−\mathrm{5}{x}\right)\right)=\mathrm{cos}\:\left(\mathrm{128}°−\mathrm{5}{x}\right) \\…
Question Number 95524 by Abdulrahman last updated on 25/May/20 $$\frac{\mathrm{1}}{\mathrm{sin10}}−\frac{\sqrt{\mathrm{3}}}{\mathrm{cos10}}=? \\ $$ Commented by PRITHWISH SEN 2 last updated on 25/May/20 $$\frac{\mathrm{cos}\:\mathrm{10}−\sqrt{\mathrm{3}}\mathrm{sin}\:\mathrm{10}}{\mathrm{sin}\:\mathrm{10cos}\:\mathrm{10}}\:=\:\mathrm{4}\frac{\left(\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\mathrm{10}−\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\mathrm{sin}\:\mathrm{10}\right)}{\mathrm{2sin}\:\mathrm{10cos}\:\mathrm{10}} \\ $$$$=\mathrm{4}.\frac{\mathrm{sin}\:\mathrm{30}.\mathrm{cos}\:\mathrm{10}−\mathrm{cos}\:\mathrm{30}.\mathrm{sin}\:\mathrm{10}}{\mathrm{sin}\:\mathrm{20}}\:=\mathrm{4}.\frac{\mathrm{sin}\:\left(\mathrm{30}−\mathrm{10}\right)}{\mathrm{sin}\:\mathrm{20}} \\…
Question Number 95495 by i jagooll last updated on 25/May/20 $$\mathrm{3cos}\:^{\mathrm{2}} {x}\:−\:\mathrm{3cos}\:{x}\:\mathrm{sin}\:{x}\:+\:\mathrm{2sin}\:{x}\:=\:\mathrm{1} \\ $$$${x}\:\in\:\left[\:\mathrm{0},\:\mathrm{2}\pi\:\right]\: \\ $$ Answered by bobhans last updated on 25/May/20 $$\mathrm{3}−\mathrm{3sin}\:^{\mathrm{2}} \mathrm{x}−\mathrm{3sin}\:\mathrm{xcos}\:\mathrm{x}\:+\mathrm{2sin}\:\mathrm{x}\:=\:\mathrm{1}…
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Question Number 29896 by ajfour last updated on 13/Feb/18 Commented by ajfour last updated on 13/Feb/18 $${At}\:{least}\:{if}\:\alpha\:=\:\beta\:=\:\gamma\:=\theta\:\left({say}\right)\:. \\ $$ Answered by mrW2 last updated on…
Question Number 95424 by john santu last updated on 25/May/20 $$\mathrm{without}\:\mathrm{calculator}\: \\ $$$$\mathrm{tan}\:^{\mathrm{2}} \mathrm{36}^{\mathrm{o}} \:×\:\mathrm{tan}\:^{\mathrm{2}} \mathrm{72}^{\mathrm{o}} \:? \\ $$ Commented by PRITHWISH SEN 2 last…