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 $${solved}\:{but}\:{could}\:{not}\:{upload}\:{image}…
Question Number 116520 by kaivan.ahmadi last updated on 04/Oct/20 $${find}\:{the}\:{center}\:{of}\:{circle}\:{with}\:{radius}\:{R} \\ $$$${and}\:{tangent}\:{by}\:{sides}\:{AB}\:{and}\:{BC}\:{of}\: \\ $$$${triangle}? \\ $$ Answered by $@y@m last updated on 04/Oct/20 $${The}\:{centre}\:{of}\:{the}\:{circle}\:{is}\:{Incentre}\:{of} \\…
Question Number 116503 by bemath last updated on 04/Oct/20 $$\mathrm{If}\:\mathrm{tan}\:\alpha\:\mathrm{and}\:\mathrm{tan}\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\: \\ $$$$\mathrm{of}\:\mathrm{equation}\:\mathrm{2x}^{\mathrm{2}} −\mathrm{5x}+\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{find}\:\begin{cases}{\mathrm{tan}\:\left(\frac{\alpha}{\mathrm{2}}+\mathrm{2}\beta\right)}\\{\mathrm{tan}\:\left(\mathrm{2}\alpha−\frac{\beta}{\mathrm{2}}\right)}\end{cases} \\ $$ Answered by bobhans last updated on 04/Oct/20 $$\Rightarrow\mathrm{x}_{\mathrm{1}}…
Question Number 116493 by bemath last updated on 04/Oct/20 $$\mathrm{Given}\:\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{sin}\:\mathrm{x}\:=\:\mathrm{1}\:,\:\mathrm{find}\: \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{cos}\:^{\mathrm{8}} \mathrm{x}+\mathrm{cos}\:^{\mathrm{6}} \mathrm{x}+\mathrm{cos}\:^{\mathrm{4}} \mathrm{x}\:=? \\ $$ Answered by bobhans last updated on 04/Oct/20…
Question Number 116483 by bemath last updated on 04/Oct/20 $$\mathrm{If}\:\mathrm{8}\:\mathrm{cos}\:\mathrm{x}−\mathrm{8}\:\mathrm{sin}\:\mathrm{x}\:=\:\mathrm{3}\:,\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\: \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{55}\:\mathrm{tan}\:\mathrm{x}\:+\:\frac{\mathrm{55}}{\mathrm{tan}\:\mathrm{x}}\:? \\ $$ Answered by mr W last updated on 04/Oct/20 $$\mathrm{8}\left(\mathrm{1}−\mathrm{tan}\:{x}\right)=\frac{\mathrm{3}}{\mathrm{cos}\:{x}} \\ $$$$\mathrm{64}\left(\mathrm{1}−\mathrm{tan}\:{x}\right)^{\mathrm{2}}…
Question Number 116448 by bobhans last updated on 04/Oct/20 $$\mathrm{If}\:\mathrm{sin}\:\left(\mathrm{P}\right)\:=\:−\frac{\mathrm{8}}{\mathrm{17}}\:,\mathrm{where}\:\frac{\mathrm{3}\pi}{\mathrm{2}}<\mathrm{P}<\mathrm{2}\pi \\ $$$$\mathrm{and}\:\mathrm{cos}\:\left(\mathrm{Q}\right)=−\frac{\mathrm{24}}{\mathrm{25}},\:\mathrm{where}\:\pi<\mathrm{Q}<\frac{\mathrm{3}\pi}{\mathrm{2}} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{cos}\:\left(\mathrm{2P}+\mathrm{Q}\right)\:=? \\ $$ Answered by bemath last updated on 04/Oct/20 $$\left(\mathrm{1}\right)\:\mathrm{cos}\:\left(\mathrm{P}\right)=\:\frac{\mathrm{15}}{\mathrm{17}}\:;\:\mathrm{sin}\:\left(\mathrm{Q}\right)=−\frac{\mathrm{7}}{\mathrm{25}} \\…