Question Number 82115 by Khyati last updated on 18/Feb/20 $${Q}.\:{Find}\:{the}\:{number}\:{of}\:{solution}\:{of}\:{thd} \\ $$$${equation}\:{tanx}\:+\:{secx}\:=\:\mathrm{2}\:{cosx}\:{lying}\:{in} \\ $$$${the}\:{interval}\:\left[\mathrm{0},\:\mathrm{2}\pi\right]\:?? \\ $$ Answered by MJS last updated on 18/Feb/20 $$\mathrm{tan}\:{x}\:+\mathrm{sec}\:{x}\:=\mathrm{2cos}\:{x} \\…
Question Number 147651 by iloveisrael last updated on 22/Jul/21 $$\:\mathrm{tan}\:\mathrm{1}°+\mathrm{tan}\:\mathrm{5}°+\mathrm{tan}\:\mathrm{9}°+…+\mathrm{tan}\:\mathrm{173}°+\mathrm{tan}\:\mathrm{177}°=? \\ $$ Commented by mr W last updated on 22/Jul/21 $$=\mathrm{45} \\ $$ Commented by…
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Question Number 82111 by john santu last updated on 18/Feb/20 $${a}\:{word}\:{is}\:{formed}\:{with}\:\mathrm{3}\:{vowels} \\ $$$${and}\:\mathrm{3}\:{consonants}\:{without}\: \\ $$$${repetition}\:.\:{the}\:{probability}\:{the} \\ $$$${formation}\:{of}\:{words}\:{begining}\:{the} \\ $$$${letter}\:{z}\:{is}? \\ $$ Commented by john santu…
Question Number 82109 by jagoll last updated on 18/Feb/20 $${what}\:{is}\:{solution} \\ $$$$\frac{{dy}}{{dx}}\:=\:\mathrm{sin}\:\left({x}+{y}\right) \\ $$ Commented by mr W last updated on 18/Feb/20 $${u}={x}+{y} \\ $$$${y}={u}−{x}…
Question Number 16572 by myintkhaing last updated on 24/Jun/17 Answered by Tinkutara last updated on 24/Jun/17 $$\left(\mathrm{i}\right)\:\mathrm{I}\:\mathrm{think}\:\mathrm{the}\:\mathrm{series}\:\mathrm{is}\:\mathrm{sin}^{\mathrm{2}} \:{x},\:\mathrm{sin}\:{x},\:\mathrm{1},\:… \\ $$$$\mathrm{It}\:\mathrm{is}\:\mathrm{a}\:\mathrm{G}.\mathrm{P}.\:\mathrm{with}\:\mathrm{common}\:\mathrm{ratio} \\ $$$$\mathrm{cosec}\:{x}. \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{7}^{\mathrm{th}} \:\mathrm{term}\:=\:{ar}^{\mathrm{6}}…
Question Number 147640 by mathdanisur last updated on 22/Jul/21 $$\mathrm{8}{sin}\left({x}\right)\:=\:\frac{\sqrt{\mathrm{3}}}{{cos}\left({x}\right)}\:+\:\frac{\mathrm{1}}{{sin}\left({x}\right)}\:\:\Rightarrow\:{x}=? \\ $$ Answered by gsk2684 last updated on 25/Jul/21 $$\mathrm{8}\:\mathrm{sin}\:^{\mathrm{2}} {x}\:\mathrm{cos}\:{x}\:=\:\sqrt{\mathrm{3}}\:\mathrm{sin}\:{x}\:+\:\mathrm{cos}\:{x} \\ $$$$\mathrm{4}\:\mathrm{sin}\:\mathrm{2}{x}\:\mathrm{sin}\:{x}\:=\:\sqrt{\mathrm{3}}\:\mathrm{sin}\:{x}\:+\:\mathrm{cos}\:{x} \\ $$$$\mathrm{2}\left(\mathrm{2}\:\mathrm{sin}\:\mathrm{2}{x}\:\mathrm{sin}\:{x}\:\right)=\:\sqrt{\mathrm{3}}\:\mathrm{sin}\:{x}\:+\:\mathrm{cos}\:{x}…
Question Number 16570 by chux last updated on 24/Jun/17 $$\mathrm{A},\mathrm{B}\:\mathrm{and}\:\mathrm{E}\:\mathrm{are}\:\mathrm{three}\:\mathrm{circles}\:\mathrm{all}\: \\ $$$$\mathrm{with}\:\mathrm{radius}\:\mathrm{1}\:\mathrm{unit}.\mathrm{A}\:\mathrm{and}\:\mathrm{E}\:\mathrm{touch} \\ $$$$\mathrm{at}\:\mathrm{P}\:\mathrm{whole}\:\mathrm{B}\:\mathrm{and}\:\mathrm{E}\:\mathrm{touch}\:\mathrm{at}\:\mathrm{Q}. \\ $$$$\angle\mathrm{POQ}=\mathrm{x}°\:\mathrm{where}\:\mathrm{O}\:\mathrm{is}\:\mathrm{the}\:\mathrm{centre}\: \\ $$$$\mathrm{of}\:\mathrm{E}.\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{overlapping}\:\mathrm{portion}\:\mathrm{of}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{if} \\ $$$$\mathrm{0}\leqslant\mathrm{x}\leqslant\mathrm{60}° \\ $$ Commented…
Question Number 147643 by bobhans last updated on 22/Jul/21 $$\:\mathrm{tan}\:\left(\mathrm{x}+\frac{\pi}{\mathrm{4}}\right)+\mathrm{3}\left(\mathrm{tan}\:\frac{\pi}{\mathrm{9}}+\mathrm{tan}\:\frac{\mathrm{2}\pi}{\mathrm{9}}\right)=\mathrm{tan}\:\left(\mathrm{x}+\frac{\pi}{\mathrm{4}}\right)\mathrm{tan}\:\frac{\pi}{\mathrm{9}}\mathrm{tan}\:\frac{\mathrm{2}\pi}{\mathrm{9}} \\ $$ Answered by liberty last updated on 22/Jul/21 $$\mathrm{tan}\:\left({x}+\frac{\pi}{\mathrm{4}}\right)−\mathrm{tan}\:\left({x}+\frac{\pi}{\mathrm{4}}\right)\mathrm{tan}\:\frac{\pi}{\mathrm{9}}\mathrm{tan}\:\frac{\mathrm{2}\pi}{\mathrm{9}}=−\mathrm{3}\left(\mathrm{tan}\:\frac{\pi}{\mathrm{9}}+\mathrm{tan}\:\frac{\mathrm{2}\pi}{\mathrm{9}}\right) \\ $$$$\mathrm{tan}\:\left({x}+\frac{\pi}{\mathrm{4}}\right)\left[\mathrm{1}−\mathrm{tan}\:\frac{\pi}{\mathrm{9}}\mathrm{tan}\:\frac{\mathrm{2}\pi}{\mathrm{9}}\right]=−\mathrm{3}\left(\mathrm{tan}\:\frac{\pi}{\mathrm{9}}+\mathrm{tan}\:\frac{\mathrm{2}\pi}{\mathrm{9}}\right) \\ $$$$\mathrm{tan}\:\left({x}+\frac{\pi}{\mathrm{4}}\right)=−\mathrm{3}\left(\frac{\mathrm{tan}\:\frac{\pi}{\mathrm{9}}+\mathrm{tan}\:\frac{\mathrm{2}\pi}{\mathrm{9}}}{\mathrm{1}−\mathrm{tan}\:\frac{\pi}{\mathrm{9}}\mathrm{tan}\:\frac{\mathrm{2}\pi}{\mathrm{9}}}\right) \\…
Question Number 82101 by legocole last updated on 18/Feb/20 $${Make}\:\mathrm{2}\:\mathrm{3}×\mathrm{3}\:{matrices}\:{i}\:{and}\:{j} \\ $$$${such}\:{that} \\ $$$${i}^{\mathrm{2}} ={j} \\ $$$${j}^{\mathrm{2}} ={i} \\ $$$${ij}=−\mathrm{1} \\ $$ Commented by Kunal12588…