Question Number 144169 by gsk2684 last updated on 22/Jun/21 $$\mathrm{please}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\mathrm{sin}\:\frac{\mathrm{2}\Pi}{\mathrm{7}}+\mathrm{sin}\:\frac{\mathrm{4}\Pi}{\mathrm{7}}+\mathrm{sin}\:\frac{\mathrm{8}\Pi}{\mathrm{7}} \\ $$ Commented by justtry last updated on 23/Jun/21 Answered by mindispower last…
Question Number 144164 by bobhans last updated on 22/Jun/21 $$\mathrm{In}\:\Delta\mathrm{ABC}\:\mathrm{given}\:\mathrm{a}=\mathrm{5},\:\mathrm{b}=\mathrm{7}\:\&\:\mathrm{c}=\:\mathrm{4}. \\ $$$$\mathrm{If}\:\measuredangle\mathrm{CAB}\:=\:\alpha\:\mathrm{then}\:\mathrm{cot}\:\left(\frac{\mathrm{1}}{\mathrm{2}}\alpha\right)=? \\ $$ Answered by liberty last updated on 22/Jun/21 $$\mathrm{cot}\:\left(\frac{\mathrm{1}}{\mathrm{2}}\alpha\right)\:=\:\sqrt{\frac{\mathrm{s}\left(\mathrm{s}−\mathrm{a}\right)}{\left(\mathrm{s}−\mathrm{b}\right)\left(\mathrm{s}−\mathrm{c}\right)}} \\ $$$$\mathrm{where}\:\mathrm{s}\:=\:\frac{\mathrm{a}+\mathrm{b}+\mathrm{c}}{\mathrm{2}}=\frac{\mathrm{5}+\mathrm{7}+\mathrm{4}}{\mathrm{2}}=\mathrm{8} \\…
Question Number 144162 by bobhans last updated on 22/Jun/21 Commented by Rasheed.Sindhi last updated on 22/Jun/21 $$\mathcal{E}{xternal}\:{angle}\:{of}\:{pentagon} \\ $$$$\:\:\:\:\:\:=\mathrm{180}−\mathrm{108}=\mathrm{72} \\ $$$${x}+\mathrm{72}+\mathrm{72}=\mathrm{180} \\ $$$${x}=\mathrm{36} \\ $$…
Question Number 144139 by bobhans last updated on 22/Jun/21 Answered by liberty last updated on 22/Jun/21 Commented by EDWIN88 last updated on 22/Jun/21 $$\frac{\mathrm{4}}{\mathrm{R}}\:=\:\frac{\mathrm{8}}{\mathrm{12}+\mathrm{R}}\:\Rightarrow\frac{\mathrm{1}}{\mathrm{R}}=\frac{\mathrm{2}}{\mathrm{12}+\mathrm{R}}\:;\:\mathrm{R}=\mathrm{12} \\…
Question Number 144086 by liberty last updated on 21/Jun/21 $$\mathrm{If}\:\mathrm{sin}\:\mathrm{t}\:+\:\mathrm{cos}\:\:\mathrm{t}\:=\:\frac{\mathrm{2}}{\mathrm{3}}\:\mathrm{then}\:\mathrm{cosec}\:\mathrm{t}+\mathrm{sec}\:\mathrm{t}\:=? \\ $$ Answered by bobhans last updated on 21/Jun/21 $$\Leftrightarrow\:\mathrm{1}+\mathrm{2sin}\:\mathrm{t}\:\mathrm{cos}\:\mathrm{t}\:=\:\frac{\mathrm{4}}{\mathrm{9}} \\ $$$$\Rightarrow\:\mathrm{2sin}\:\mathrm{t}\:\mathrm{cos}\:\mathrm{t}\:=−\frac{\mathrm{5}}{\mathrm{9}} \\ $$$$\Rightarrow\mathrm{sin}\:\mathrm{t}\:\mathrm{cos}\:\mathrm{t}\:=−\frac{\mathrm{5}}{\mathrm{18}} \\…
Question Number 131492 by Ar Brandon last updated on 05/Feb/21 $$\mathrm{sin}^{\mathrm{4}} \frac{\pi}{\mathrm{16}}+\mathrm{sin}^{\mathrm{4}} \frac{\mathrm{3}\pi}{\mathrm{16}}+\mathrm{sin}^{\mathrm{4}} \frac{\mathrm{5}\pi}{\mathrm{16}}+\mathrm{sin}^{\mathrm{4}} \frac{\mathrm{7}\pi}{\mathrm{16}} \\ $$ Answered by Dwaipayan Shikari last updated on 05/Feb/21…
Question Number 65929 by Masumsiddiqui399@gmail.com last updated on 06/Aug/19 Commented by kaivan.ahmadi last updated on 06/Aug/19 $${cot}\mathrm{1}={tan}\mathrm{89} \\ $$$${cot}\mathrm{2}={tan}\mathrm{88} \\ $$$$\vdots \\ $$$${cot}\mathrm{44}={tan}\mathrm{46} \\ $$$${since}\:\:{tan}\left(\frac{\pi}{\mathrm{2}}−\alpha\right)={cot}\alpha…
Question Number 131301 by liberty last updated on 03/Feb/21 $$\mathrm{cos}^{−\mathrm{1}} \sqrt{\mathrm{x}^{\mathrm{3}} −\mathrm{x}+\mathrm{1}}\:+\mathrm{cos}^{−\mathrm{1}} \:\sqrt{\mathrm{x}−\mathrm{x}^{\mathrm{3}} }\:+\:\mathrm{cos}^{−\mathrm{1}} \:\sqrt{\mathrm{1}−\mid\mathrm{y}\mid}\:=\:\frac{\mathrm{2}\pi}{\mathrm{3}} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{y}\: \\ $$ Answered by EDWIN88 last updated on…
Question Number 131296 by EDWIN88 last updated on 03/Feb/21 $$\:{If}\:{a}\mathrm{sin}^{−\mathrm{1}} \left({x}\right)−{b}\mathrm{cos}^{−\mathrm{1}} \left({x}\right)=\:{c}\: \\ $$$${then}\:{the}\:{value}\:{of}\:{a}\mathrm{sin}^{−\mathrm{1}} \left({x}\right)+{b}\mathrm{cos}^{−\mathrm{1}} \left({x}\right)\: \\ $$$$\left({whenever}\:{exists}\right)\:{is}\:{equal}\:{to}\:? \\ $$ Answered by liberty last updated…
Question Number 131302 by EDWIN88 last updated on 03/Feb/21 $${Given}\:\mathrm{sin}\:\left(\frac{\pi}{\mathrm{6}}+\mathrm{tan}^{−\mathrm{1}} \left({x}\right)\right)=\:\frac{\mathrm{13}}{\mathrm{14}} \\ $$$$\:{If}\:\mathrm{tan}^{−\mathrm{1}} \left({x}\right)=\:\mathrm{tan}^{−\mathrm{1}} \left(\frac{{a}\sqrt{\mathrm{3}}}{{b}}\right)\:{then}\: \\ $$$$\:\frac{{a}+{b}}{\mathrm{2}}\:=?\: \\ $$ Answered by mr W last updated…