Question Number 7142 by Tawakalitu. last updated on 13/Aug/16 $${The}\:{sides}\:{of}\:{a}\:{triangle}\:{are}\:{x}\:{cm},\:\left({x}\:−\:\mathrm{4}\right)\:{cm},\:\left({x}\:−\:\mathrm{8}\right){cm} \\ $$$${respectively}\:.\:{if}\:{the}\:{cosine}\:{o}\:{the}\:{largest}\:{is}\:\frac{\mathrm{1}}{\mathrm{5}}\:,\: \\ $$$${calculate}\:{the}\:{angles}\:{of}\:\:{triangle}. \\ $$$$ \\ $$ Answered by Rasheed Soomro last updated on…
Question Number 7055 by Tawakalitu. last updated on 08/Aug/16 $${Show}\:{that}\:\forall\:{x}\:\in\:\left[\:\mathrm{0},\:\frac{\Pi}{\mathrm{2}}\:\right]\:,\:{tanx}\:+\:{sin}\mathrm{4}{x}\:\geqslant\:\mathrm{0}\: \\ $$$$ \\ $$ Commented by Yozzii last updated on 08/Aug/16 $${If}\:\mathrm{0}\leqslant{x}\leqslant\frac{\pi}{\mathrm{2}}\Rightarrow\mathrm{0}\leqslant\mathrm{4}{x}\leqslant\mathrm{2}\pi \\ $$$${For}\:−\mathrm{1}\leqslant{sin}\mathrm{4}{x}<\mathrm{0}\Rightarrow\pi<\mathrm{4}{x}\leqslant\frac{\mathrm{3}\pi}{\mathrm{2}}\:{or}\:\frac{\mathrm{3}\pi}{\mathrm{2}}\leqslant\mathrm{4}{x}<\mathrm{2}\pi\: \\…
Question Number 7039 by Rasheed Soomro last updated on 07/Aug/16 $${Show}\:{without}\:{using}\:{calculator}\:{that} \\ $$$$\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{sin}\:\mathrm{20sin}\:\mathrm{150sin}\:\mathrm{160}}{\mathrm{sin}\:\mathrm{10}\:\mathrm{sin}\:\mathrm{140}+\mathrm{sin}\:\mathrm{20}\:\mathrm{sin}\:\mathrm{150}\:\mathrm{cos}\:\mathrm{160}}\right)=\mathrm{130} \\ $$ Commented by Yozzii last updated on 08/Aug/16 $${All}\:{figures}\:{are}\:{assumed}\:{to}\:{be}\:{in}\:{degrees}. \\…
Question Number 138099 by liberty last updated on 10/Apr/21 $${If}\:\mathrm{sin}\:^{\mathrm{4}} \alpha+\mathrm{cos}\:^{\mathrm{4}} \beta\:=\:\mathrm{4sin}\:\alpha\:\mathrm{cos}\:\beta\:, \\ $$$$\mathrm{0}\leqslant\alpha,\beta\:\leqslant\:\frac{\pi}{\mathrm{2}}\:,\:{then}\:\mathrm{sin}\:\alpha+\mathrm{cos}\:\beta\: \\ $$$${equal}\:{to}\:\ldots \\ $$ Commented by mr W last updated on…
Question Number 72497 by Shamim last updated on 29/Oct/19 $$\mathrm{if},\:\mathrm{cot}\:\theta+\mathrm{cosec}\:\theta=\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:\theta\:\mathrm{where}\:\mathrm{0}<\theta\leqslant\mathrm{2}\pi. \\ $$ Answered by behi83417@gmail.com last updated on 29/Oct/19 $$\frac{\mathrm{cos}\theta}{\mathrm{sin}\theta}+\frac{\mathrm{1}}{\mathrm{sin}\theta}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}\Rightarrow\frac{\mathrm{1}+\mathrm{cos}\theta}{\mathrm{sin}\theta}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}\Rightarrow \\ $$$$\frac{\mathrm{2cos}^{\mathrm{2}} \frac{\theta}{\mathrm{2}}}{\mathrm{2sin}\frac{\theta}{\mathrm{2}}\mathrm{cos}\frac{\theta}{\mathrm{2}}}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}\Rightarrow\begin{cases}{\mathrm{1}.\mathrm{cos}\frac{\theta}{\mathrm{2}}=\mathrm{0}}\\{\mathrm{2}.\mathrm{cot}\frac{\theta}{\mathrm{2}}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}}\end{cases}…
Question Number 72492 by petrochengula last updated on 29/Oct/19 $$\frac{\mathrm{1}}{\mathrm{cosx}}+\frac{\mathrm{1}}{\mathrm{sinx}}=\mathrm{8} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x} \\ $$ Commented by petrochengula last updated on 29/Oct/19 $$\mathrm{help}\:\mathrm{please} \\ $$ Answered…
Question Number 6908 by Tawakalitu. last updated on 02/Aug/16 $${sin}\left({Z}\right)\:=\:\mathrm{100} \\ $$$$ \\ $$$${find}\:{z}\: \\ $$ Commented by Rasheed Soomro last updated on 02/Aug/16 $${Always}…
Question Number 6890 by Tawakalitu. last updated on 01/Aug/16 Commented by Yozzii last updated on 02/Aug/16 $${Let}\:{EC}={x}.\:{BD}=\mathrm{3},\:{DA}=\mathrm{5} \\ $$$${BD}={BE}\:{since}\:{BD}\:{and}\:{BE}\:{are}\:{lines} \\ $$$${tangent}\:{to}\:{the}\:{same}\:{circle}\:{from}\: \\ $$$${the}\:{common}\:{point}\:{B}. \\ $$$$\therefore\:{BE}=\mathrm{3}.\:{Similarly},\:{DA}={AF}=\mathrm{5},…
Question Number 6872 by hanandmishra026@gmail.com last updated on 31/Jul/16 $${Eliminate}\:\theta\:\:{if}\:{x}={a}\:\mathrm{sec}^{\mathrm{3}} \theta\:{and}\:\:{y}={b}\:\mathrm{tan}^{\mathrm{3}} \theta \\ $$ Commented by Yozzii last updated on 31/Jul/16 $${sec}\theta=\left(\frac{{x}}{{a}}\right)^{\mathrm{1}/\mathrm{3}} ,\:{tan}\theta=\left(\frac{{y}}{{b}}\right)^{\mathrm{1}/\mathrm{3}} \\ $$$${sec}^{\mathrm{2}}…
Question Number 6852 by Tawakalitu. last updated on 31/Jul/16 Commented by Tawakalitu. last updated on 31/Jul/16 $${Please}\:{i}\:{need}\:{solution}\:{here}….\:{to}\:{solve}\:{for}\:{x} \\ $$ Answered by Rasheed Soomro last updated…