Question Number 116891 by bemath last updated on 07/Oct/20 $$\mathrm{Proof}\:\mathrm{that}\:\frac{\mathrm{4}\left(\mathrm{cos}\:^{\mathrm{4}} \left({a}\right)+\mathrm{sin}\:^{\mathrm{4}} \left({a}\right)\right)}{\mathrm{cos}\:^{\mathrm{4}} \left({a}\right)−\mathrm{sin}\:^{\mathrm{4}} \left({a}\right)}\:=\:\left(\mathrm{3}+\mathrm{cos}\:\left(\mathrm{4}{a}\right)\right)\mathrm{sec}\:\left(\mathrm{2}{a}\right)\: \\ $$ Answered by john santu last updated on 07/Oct/20 $$\Rightarrow\:\frac{\mathrm{4}\left\{\left(\mathrm{sin}\:^{\mathrm{2}}…
Question Number 51356 by rahul 19 last updated on 26/Dec/18 $${Evaluate}\:: \\ $$$$\mathrm{tan}\:\left\{\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}^{−\mathrm{1}} \frac{\sqrt{\mathrm{5}}}{\mathrm{3}}\right\}\:? \\ $$ Commented by rahul 19 last updated on 26/Dec/18 $${Ans}\rightarrow\:\frac{\mathrm{3}−\sqrt{\mathrm{5}}}{\mathrm{2}}.…
Question Number 116832 by bemath last updated on 07/Oct/20 $$\mathrm{If}\:\mathrm{19}\:\mathrm{sin}\:\mathrm{2x}\:=\:\mathrm{37}\:\mathrm{cos}\:\mathrm{2x}+\mathrm{38}\:\mathrm{sin}\:^{\mathrm{2}} \mathrm{x} \\ $$$$\mathrm{then}\:\mathrm{tan}\:\mathrm{x}\:=\:\_\_ \\ $$ Answered by bobhans last updated on 07/Oct/20 $$\Rightarrow\mathrm{19}\:\mathrm{sin}\:\mathrm{2x}\:=\:\mathrm{37}\:\mathrm{cos}\:\mathrm{2x}+\mathrm{38sin}\:^{\mathrm{2}} \mathrm{x} \\…
Question Number 182332 by mnjuly1970 last updated on 07/Dec/22 $$ \\ $$$$\mathrm{If}\:\:,\:\:\:{f}\:\left({x}\right)\:=\:\mathrm{2}{cos}^{\:\mathrm{2}} \left(\frac{{x}}{\mathrm{2}}\right)\:−\lfloor\:\frac{\mathrm{1}}{\mathrm{3}}\:+{cos}\left({x}\right)\:\rfloor \\ $$$$\:\:{then}\:{find}\:{the}\:{range}\:{of}\::\:\:\:{R}_{\:{f}} \\ $$ Answered by floor(10²Eta[1]) last updated on 07/Dec/22 $$−\mathrm{1}\leqslant\mathrm{cosx}\leqslant\mathrm{1}\Rightarrow\frac{−\mathrm{2}}{\mathrm{3}}\leqslant\frac{\mathrm{1}}{\mathrm{3}}+\mathrm{cosx}\leqslant\frac{\mathrm{4}}{\mathrm{3}}…
Question Number 116768 by bemath last updated on 06/Oct/20 $$\mathrm{sin}\:\left(\mathrm{4sin}^{−\mathrm{1}} \left(\mathrm{x}\right)\right)\:=\:\mathrm{sin}\:\left(\mathrm{2sin}^{−\mathrm{1}} \left(\mathrm{x}\right)\right) \\ $$ Answered by bobhans last updated on 06/Oct/20 $$\mathrm{letting}\:\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{x}\right)\:=\:\mathrm{z}\Rightarrow\mathrm{sin}\:\mathrm{z}\:=\:\mathrm{x} \\ $$$$\Rightarrow\:\mathrm{sin}\:\left(\mathrm{4z}\right)\:=\:\mathrm{sin}\:\left(\mathrm{2z}\right)\:…
Question Number 51150 by peter frank last updated on 24/Dec/18 $${from}\:{left}\:{hand}\:{sides} \\ $$$${prove}\:{that} \\ $$$$\frac{{sin}\alpha\mathrm{sin}\:\beta}{\mathrm{cos}\:\alpha+\mathrm{cos}\:\beta}=\frac{\mathrm{2tan}\frac{\alpha}{\mathrm{2}}\:\mathrm{tan}\:\frac{\beta}{\mathrm{2}}}{\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}} \frac{\alpha}{\mathrm{2}}\mathrm{tan}^{\mathrm{2}} \:\frac{\beta}{\mathrm{2}}} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on…
Question Number 116630 by bobhans last updated on 05/Oct/20 $$\mathrm{Given}\:\mathrm{cosec}\:\mathrm{x}\:+\:\mathrm{cot}\:\mathrm{x}\:=\:\mathrm{p}\:,\:\mathrm{find}\:\mathrm{the}\: \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{cosec}\:\mathrm{x}\:=? \\ $$ Answered by TANMAY PANACEA last updated on 05/Oct/20 $$\mathrm{1}+{cot}^{\mathrm{2}} {x}={cosec}^{\mathrm{2}} {x}…
Question Number 51069 by rahul 19 last updated on 23/Dec/18 $${If}\:\mathrm{sin}{A}+\mathrm{cos2}{A}\:=\frac{\mathrm{1}}{\mathrm{2}}\:{and} \\ $$$$\mathrm{cos}{A}+\mathrm{sin2}{A}=\frac{\mathrm{1}}{\mathrm{3}}\:,\:{then}\:{find}\:{the}\:{value} \\ $$$${of}\:\mathrm{sin3}{A}. \\ $$ Answered by peter frank last updated on 23/Dec/18…
Question Number 50996 by rahul 19 last updated on 23/Dec/18 $${Find}\:{the}\:{minimum}\:{value}\:{of} \\ $$$${f}\left({x}\right)=\:\mathrm{9tan}^{\mathrm{2}} \theta+\mathrm{4cot}^{\mathrm{2}} \theta\:? \\ $$ Commented by rahul 19 last updated on 23/Dec/18…
Question Number 116524 by abdullahquwatan last updated on 04/Oct/20 $$\mathrm{if}\:\alpha+\beta+\gamma=\mathrm{180}° \\ $$$$\mathrm{prove}: \\ $$$$\mathrm{sin}\:\alpha+\mathrm{sin}\:\beta+\mathrm{sin}\:\gamma+\mathrm{sin}\:\frac{\pi}{\mathrm{3}}\:<\:\mathrm{4}\:\mathrm{sin}\:\frac{\pi}{\mathrm{3}} \\ $$ Commented by TANMAY PANACEA last updated on 04/Oct/20 $${solved}\:{but}\:{could}\:{not}\:{upload}\:{image}…