Question Number 15555 by Tinkutara last updated on 11/Jun/17 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{cos}\:\mathrm{8}{x}\:−\:\mathrm{cos}\:\mathrm{7}{x}}{\mathrm{1}\:+\:\mathrm{2}\:\mathrm{cos}\:\mathrm{5}{x}}\:=\:\mathrm{cos}\:\mathrm{3}{x}\:−\:\mathrm{cos}\:\mathrm{2}{x} \\ $$ Answered by ajfour last updated on 11/Jun/17 $${considering} \\ $$$${f}\left({x}\right)=\left(\mathrm{1}+\mathrm{2cos}\:\mathrm{5}{x}\right)\left(\mathrm{cos}\:\mathrm{3}{x}−\mathrm{cos}\:\mathrm{2}{x}\right) \\…
Question Number 81062 by john santu last updated on 09/Feb/20 $$\mathrm{cos}\:{x}\:\sqrt{\mathrm{1}+\mathrm{sin}\:{x}−\mathrm{2cos}\:{x}}\:=\:\mathrm{cos}\:{x}−\mathrm{sin}\:{x} \\ $$$${in}\:\left[\:−\mathrm{5}\pi\:,\:−\frac{\mathrm{7}\pi}{\mathrm{2}}\right]\: \\ $$ Commented by MJS last updated on 09/Feb/20 $$\mathrm{sorry}\:\mathrm{no}\:\mathrm{time}\:\mathrm{today} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{let}\:{x}=\mathrm{2arctan}\:{t}…
Question Number 81057 by mathocean1 last updated on 09/Feb/20 $${solve}\:\mathrm{in}\:\left[−\pi;\pi\right]\: \\ $$$$\left({E}\right):\:{sin}\mathrm{3}{x}=−{sin}\mathrm{2}{x} \\ $$ Commented by jagoll last updated on 09/Feb/20 $$\mathrm{sin}\:\mathrm{3}{x}+\mathrm{sin}\:\mathrm{2}{x}\:=\mathrm{0} \\ $$$$\mathrm{2sin}\:\left(\frac{\mathrm{5}{x}}{\mathrm{2}}\right)\mathrm{cos}\:\left(\frac{{x}}{\mathrm{2}}\right)=\mathrm{0} \\…
Question Number 15471 by Mr easymsn last updated on 10/Jun/17 Answered by sma3l2996 last updated on 10/Jun/17 $$\left({a}\right) \\ $$$$\mathrm{2}{sin}\left({x}\right){cos}\left({x}\right)+{sinx}=\mathrm{1}−\mathrm{2}{cos}^{\mathrm{2}} {x}−{cosx} \\ $$$${sin}\left({x}\right)\left(\mathrm{2}{cos}\left({x}\right)+\mathrm{1}\right)=\mathrm{1}−\mathrm{2}{cos}^{\mathrm{2}} {x}−{cosx} \\…
Question Number 80998 by Power last updated on 08/Feb/20 Commented by mr W last updated on 08/Feb/20 $${just}\:{as}\:{for}\:{a}\:{lot}\:{of}\:{your}\:{other}\:{questions}, \\ $$$${you}\:{also}\:{need}\:{a}\:{calculator}\:{for}\:{this}\:{one}. \\ $$ Answered by jagoll…
Question Number 81003 by mathocean1 last updated on 08/Feb/20 $$\left(\mathrm{E}\right):\:\mathrm{sin2}{x}={cosx}+{sinx}−\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{1}.\:{show}\:{that}\:\left(\mathrm{E}\right)\:\mathrm{is}\:\mathrm{equivalent}\:\mathrm{to}\: \\ $$$$\left(\mathrm{E}'\right):\:\mathrm{2cos}^{\mathrm{2}} \mathrm{X}−\sqrt{\mathrm{2}}\mathrm{cosX}−\frac{\mathrm{1}}{\mathrm{2}}=\mathrm{0} \\ $$$$\mathrm{with}\:\mathrm{X}={x}−\frac{\pi}{\mathrm{4}}. \\ $$ Commented by MJS last updated on…
Question Number 80941 by jagoll last updated on 08/Feb/20 $$\mathrm{cos}\:{x}−\mathrm{2cos}\:{y}=−\sqrt{\mathrm{3}} \\ $$$$\mathrm{sin}\:\left({x}−{y}\right)=\frac{\mathrm{2}\sqrt{\mathrm{2}}}{\mathrm{3}} \\ $$$${what}\:{is}\:\mathrm{sin}\:{x}−\mathrm{2sin}\:{y}\:? \\ $$ Commented by john santu last updated on 08/Feb/20 $${let}\:\mathrm{sin}\:{x}−\mathrm{2sin}\:{y}\:=\:{t}…
Question Number 15393 by Tinkutara last updated on 10/Jun/17 $$\mathrm{A}\:\mathrm{man}\:\mathrm{observes}\:\mathrm{that}\:\mathrm{when}\:\mathrm{he}\:\mathrm{moves}\:\mathrm{up} \\ $$$$\mathrm{a}\:\mathrm{distance}\:{c}\:\mathrm{metres}\:\mathrm{on}\:\mathrm{a}\:\mathrm{slope},\:\mathrm{the} \\ $$$$\mathrm{angle}\:\mathrm{of}\:\mathrm{depression}\:\mathrm{of}\:\mathrm{a}\:\mathrm{point}\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{horizontal}\:\mathrm{plane}\:\mathrm{from}\:\mathrm{the}\:\mathrm{base}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{slope}\:\mathrm{is}\:\mathrm{30}°,\:\mathrm{and}\:\mathrm{when}\:\mathrm{he}\:\mathrm{moves}\:\mathrm{up} \\ $$$$\mathrm{further}\:\mathrm{a}\:\mathrm{distance}\:{c}\:\mathrm{metres},\:\mathrm{the}\:\mathrm{angle}\:\mathrm{of} \\ $$$$\mathrm{depression}\:\mathrm{of}\:\mathrm{that}\:\mathrm{point}\:\mathrm{is}\:\mathrm{45}°.\:\mathrm{The} \\ $$$$\mathrm{angle}\:\mathrm{of}\:\mathrm{inclination}\:\mathrm{of}\:\mathrm{the}\:\mathrm{slope}\:\mathrm{with}\:\mathrm{the} \\…
Question Number 15392 by Tinkutara last updated on 10/Jun/17 $$\mathrm{Each}\:\mathrm{side}\:\mathrm{of}\:\mathrm{an}\:\mathrm{equilateral}\:\mathrm{triangle} \\ $$$$\mathrm{subtends}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{60}°\:\mathrm{at}\:\mathrm{the}\:\mathrm{top}\:\mathrm{of}\:\mathrm{a} \\ $$$$\mathrm{tower}\:\mathrm{of}\:\mathrm{height}\:{h}\:\mathrm{standing}\:\mathrm{at}\:\mathrm{the}\:\mathrm{centre} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}.\:\mathrm{If}\:\mathrm{2}{a}\:\mathrm{be}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{side}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle},\:\mathrm{then}\:\frac{{a}^{\mathrm{2}} }{{h}^{\mathrm{2}} }\:=\:? \\ $$ Answered by mrW1…
Question Number 80929 by mathocean1 last updated on 08/Feb/20 $$\mathrm{show}\:\mathrm{that} \\ $$$${cos}\frac{\pi}{\mathrm{7}}\mathrm{cos}\frac{\mathrm{2}\pi}{\mathrm{7}}\mathrm{cos}\frac{\mathrm{4}\pi}{\mathrm{7}}=−\frac{\mathrm{1}}{\mathrm{8}} \\ $$ Commented by jagoll last updated on 08/Feb/20 $${let}\:{x}\:=\frac{\pi}{\mathrm{7}} \\ $$$$\mathrm{cos}\:{x}\mathrm{cos}\:\mathrm{2}{x}\mathrm{cos}\:\mathrm{4}{x}\:×\frac{\mathrm{2sin}\:{x}}{\mathrm{2sin}\:{x}}\:= \\…