Question Number 3584 by prakash jain last updated on 16/Dec/15 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{a}\:\mathrm{regular}\:\mathrm{pentagon}\:\mathrm{diagonal} \\ $$$$\mathrm{to}\:\mathrm{its}\:\mathrm{side}\:\mathrm{is}\:\frac{\sqrt{\mathrm{5}}+\mathrm{1}}{\mathrm{2}}. \\ $$ Commented by Yozzii last updated on 15/Dec/15 $${Its}\:{side}\:{is}\:{one}\:{of}\:{the}\:\mathrm{5}\:\:{edges}? \\ $$$$\:\:\:\:\:\:\:\:\:\:{a}\:\:\:\:\:\:\:\:{b}…
Question Number 69081 by myintkhaing1121960@gmail.com last updated on 19/Sep/19 $${prove}\:{that} \\ $$$${tan}\:\frac{\mathrm{3}\pi}{\mathrm{7}}\:−\mathrm{4}{sin}\:\frac{\pi}{\mathrm{7}}\:=\:\sqrt{\mathrm{7}}. \\ $$ Answered by Tanmay chaudhury last updated on 19/Sep/19 $$\mathrm{7}{a}=\pi \\ $$$${tan}\mathrm{7}{a}={tan}\pi=−\mathrm{0}…
Question Number 134581 by EDWIN88 last updated on 05/Mar/21 $$\mathrm{Given}\:\begin{cases}{\mathrm{sin}\:\mathrm{A}+\mathrm{sin}\:\mathrm{B}=\mathrm{0}.\mathrm{7}}\\{\mathrm{cos}\:\mathrm{A}+\mathrm{cos}\:\mathrm{B}=\mathrm{0}.\mathrm{8}}\end{cases} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}. \\ $$ Answered by liberty last updated on 05/Mar/21 $$\Leftrightarrow\:\mathrm{2}+\mathrm{2cos}\:\left(\mathrm{A}−\mathrm{B}\right)=\:\frac{\mathrm{49}+\mathrm{64}}{\mathrm{100}} \\ $$$$\Leftrightarrow\mathrm{2cos}\:\left(\mathrm{A}−\mathrm{B}\right)\:=\:−\frac{\mathrm{87}}{\mathrm{100}} \\…
Question Number 69034 by ahmadshah last updated on 18/Sep/19 Answered by $@ty@m123 last updated on 18/Sep/19 $$\mathrm{4cos}\:{x}−\mathrm{3sec}\:{x}−\mathrm{2tan}\:{x} \\ $$$$\mathrm{4cos}\:{x}−\frac{\mathrm{3}}{\mathrm{cos}\:{x}}−\frac{\mathrm{2sin}\:{x}}{\mathrm{cos}\:{x}} \\ $$$$=\frac{\mathrm{4cos}\:^{\mathrm{2}} {x}−\mathrm{3}−\mathrm{2sin}\:{x}}{\mathrm{cos}\:{x}} \\ $$$$=\frac{\mathrm{4cos}\:^{\mathrm{3}} {x}−\mathrm{3cos}\:{x}−\mathrm{2sin}\:{x}\mathrm{cos}\:{x}}{\mathrm{cos}^{\mathrm{2}}…
Question Number 134538 by bemath last updated on 05/Mar/21 $$ \\ $$How do you find the interval in which x belongs such that |sinx+cosx|=sinx +…
Question Number 68991 by pranay02 last updated on 17/Sep/19 $${if}\:{the}\:{range}\:{of}\:{f}\left({x},\:{y}\right)\:=\:{sec}^{−\mathrm{1}} \left({x}+\frac{\mathrm{1}}{{x}}\right)+{sec}^{−\mathrm{1}} \left({y}+\frac{\mathrm{1}}{{y}}\right),\:{xy}<\mathrm{0}\:{is}\:\left({a},\:{b}\right)\:{and}\:\left({a}+{b}\right)\:{equals}\:\frac{\lambda\pi}{\mathrm{10}},\:{then}\:\lambda\:{is}\:{eqal}\:{to}\: \\ $$ Answered by MJS last updated on 18/Sep/19 $${g}\left({t}\right)=\mathrm{sec}^{−\mathrm{1}} \:\left({t}+\frac{\mathrm{1}}{{t}}\right)\:=\mathrm{cos}^{−\mathrm{1}} \:\left(\frac{{t}}{{t}^{\mathrm{2}} +\mathrm{1}}\right)…
Question Number 68964 by ahmadshah last updated on 17/Sep/19 Commented by mind is power last updated on 17/Sep/19 $${m}+{in}={e}^{{ia}} +{e}^{{ib}} \Rightarrow{m}^{\mathrm{2}} −{n}^{\mathrm{2}} +\mathrm{2}{imn}={e}^{{i}\mathrm{2}{a}} +{e}^{\mathrm{2}{ib}} +\mathrm{2}{e}^{{i}\left({a}+{b}\right)}…
Question Number 134479 by abdullahquwatan last updated on 04/Mar/21 $$\mathrm{sin}\:\mathrm{x}+\mathrm{sin}\:\mathrm{2x}+\mathrm{sin}\:\mathrm{3x}=\mathrm{cos}\:\mathrm{x}+\mathrm{2cos}\:^{\mathrm{2}} \mathrm{x} \\ $$$$\mathrm{0}<\mathrm{x}<\pi \\ $$ Answered by EDWIN88 last updated on 14/Mar/21 $$\mathrm{sin}\:\mathrm{3x}+\mathrm{sin}\:\mathrm{x}\:=\:\mathrm{2sin}\:\mathrm{2x}\:\mathrm{cos}\:\mathrm{x} \\ $$$$\left(\bullet\right)\mathrm{2sin}\:\mathrm{2x}\:\mathrm{cos}\:\mathrm{x}\:+\:\mathrm{sin}\:\mathrm{2x}\:=\:\mathrm{cos}\:\mathrm{x}\left(\mathrm{1}+\mathrm{2cos}\:\mathrm{x}\right)…
Question Number 134475 by EDWIN88 last updated on 04/Mar/21 $$\mathrm{If}\:\mathrm{1}+\mathrm{cos}\:\mathrm{x}+\mathrm{cos}\:\mathrm{2x}+\mathrm{cos}\:\mathrm{3x}+\mathrm{cos}\:\mathrm{4x}+…+\infty\:=\:\mathrm{3} \\ $$$$\mathrm{for}\:\mathrm{0}<\mathrm{x}\leqslant\frac{\pi}{\mathrm{2}} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{sin}\:\mathrm{x}+\mathrm{sin}\:\mathrm{2x}+\mathrm{sin}\:\mathrm{3x}+…+\infty \\ $$ Commented by Dwaipayan Shikari last updated on 04/Mar/21 $$\underset{{n}=\mathrm{0}}…
Question Number 134464 by bramlexs22 last updated on 04/Mar/21 $$\:\:\:\:\:\:\:\begin{array}{|c|c|}{\mathrm{Solve}\:\mathrm{the}\:\mathrm{following}\:\mathrm{Equation}}\\{\:\:\mathrm{81}^{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}} \:+\:\mathrm{81}^{\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}} \:=\:\mathrm{30}\:}\\\hline\end{array} \\ $$ Commented by harckinwunmy last updated on 04/Mar/21 $${ff} \\…