Question Number 78427 by Chi Mes Try last updated on 17/Jan/20 $${please}\:{i}\:{need}\:{it}\:{urgently} \\ $$$$ \\ $$$${show}\:{that}\:{the}\:{midpoint}\:{of}\:{the}\:{hypotenuse} \\ $$$${of}\:{a}\:{right}\:{triangle}\:{is}\:{equidistant}\:{from}\:{its}\:{vertices} \\ $$ Answered by MJS last updated…
Question Number 143959 by bobhans last updated on 20/Jun/21 $$\:\:\mathrm{If}\:\mathrm{g}\left(\mathrm{x}\right)=\left(\mathrm{4cos}\:^{\mathrm{4}} \mathrm{x}−\mathrm{2cos}\:\mathrm{2x}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\mathrm{4x}−\mathrm{x}^{\mathrm{7}} \right)^{\frac{\mathrm{1}}{\mathrm{7}}} \\ $$$$\mathrm{then}\:\mathrm{tbe}\:\mathrm{value}\:\mathrm{of}\:\mathrm{g}\left(\mathrm{g}\left(\mathrm{100}\right)\right)\:\mathrm{is} \\ $$$$\mathrm{equal}\:\mathrm{to}\:… \\ $$ Answered by Olaf_Thorendsen last updated on 20/Jun/21…
Question Number 143958 by bobhans last updated on 20/Jun/21 Answered by bramlex last updated on 20/Jun/21 $$\Rightarrow\:\begin{cases}{\mathrm{sin}\:^{\mathrm{2}} \alpha+\mathrm{2sin}\:\alpha\mathrm{sin}\:\beta+\mathrm{sin}\:^{\mathrm{2}} \beta=\mathrm{9}{p}}\\{\mathrm{cos}\:^{\mathrm{2}} \alpha+\mathrm{2cos}\:\alpha\mathrm{cos}\:\beta+\mathrm{cos}\:^{\mathrm{2}} \beta=\mathrm{9}{q}}\end{cases} \\ $$$$\Leftrightarrow\mathrm{2}+\mathrm{2cos}\:\left(\alpha−\beta\right)=\mathrm{9}\left({p}+{q}\right)\: \\ $$$$\Leftrightarrow\:\mathrm{2cos}\:\left(\alpha−\beta\right)=\mathrm{9}\left({p}+{q}\right)−\mathrm{2}…
Question Number 78395 by john santu last updated on 17/Jan/20 $${what}\:{minimum}\:{value}\:{of}\: \\ $$$${y}\:=\:\mathrm{sin}\:{x}+\mathrm{cosec}\:{x}+\mathrm{2}\: \\ $$ Commented by jagoll last updated on 17/Jan/20 $${let}\:\mathrm{sin}\:{x}={t} \\ $$$${y}={t}\:+\frac{\mathrm{1}}{{t}}+\mathrm{2}…
Question Number 143923 by Sravanth last updated on 19/Jun/21 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\left[\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{sin}\left(\frac{\mathrm{2}\pi}{\mathrm{3}}\right)\right)\right]? \\ $$ Commented by mr W last updated on 19/Jun/21 $$\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{sin}\left(\frac{\mathrm{2}\pi}{\mathrm{3}}\right)\right)=\frac{\pi}{\mathrm{3}} \\ $$…
Question Number 143913 by Sravanth last updated on 19/Jun/21 $$\mathrm{If}\:\:\frac{\mathrm{cos}\:\alpha}{{cos}\:\beta}\:=\:\mathrm{m}\:\mathrm{and}\:\frac{\mathrm{cos}\:\alpha}{\mathrm{sin}\:\beta}\:=\:\mathrm{n}\:\mathrm{then} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\left(\mathrm{m}^{\mathrm{2}} +\mathrm{n}^{\mathrm{2}} \right)\mathrm{cos}^{\mathrm{2}} \beta\:=\:{n}^{\mathrm{2}} \\ $$ Answered by Ar Brandon last updated on 19/Jun/21…
Question Number 143897 by liberty last updated on 19/Jun/21 Answered by bobhans last updated on 19/Jun/21 $$\:\:\mathrm{sin}\:^{\mathrm{2}} \:\frac{\pi}{\mathrm{8}}+\mathrm{cos}\:^{\mathrm{2}} \:\frac{\pi}{\mathrm{8}}+\mathrm{cos}\:^{\mathrm{2}} \:\frac{\mathrm{5}\pi}{\mathrm{8}}+\mathrm{sin}\:^{\mathrm{2}} \:\frac{\mathrm{5}\pi}{\mathrm{8}}=\mathrm{2} \\ $$ Terms of…
Question Number 143856 by gsk2684 last updated on 19/Jun/21 $$\mathrm{if}\:\frac{\mathrm{cos}^{\mathrm{4}} \mathrm{x}}{\mathrm{cos}^{\mathrm{2}} \mathrm{y}}+\frac{\mathrm{sin}^{\mathrm{4}} \mathrm{x}}{\mathrm{sin}^{\mathrm{2}} \mathrm{y}}=\mathrm{1then}\:\mathrm{find}\: \\ $$$$\:\frac{\mathrm{cos}^{\mathrm{4}} \mathrm{y}}{\mathrm{cos}^{\mathrm{2}} \mathrm{x}}+\frac{\mathrm{sin}^{\mathrm{4}} \mathrm{y}}{\mathrm{sin}^{\mathrm{2}} \mathrm{x}} \\ $$ Commented by justtry…
Question Number 143857 by gsk2684 last updated on 19/Jun/21 $$\mathrm{if}\:\mathrm{cos}^{\mathrm{4}} \theta\mathrm{sec}\:^{\mathrm{2}} \alpha,\:\frac{\mathrm{1}}{\mathrm{2}},\:\mathrm{sin}^{\mathrm{4}} \theta\mathrm{cosec}^{\mathrm{2}} \alpha\: \\ $$$$\mathrm{are}\:\mathrm{in}\:\mathrm{A}.\mathrm{P}.\:\mathrm{then} \\ $$$$\:\mathrm{cos}^{\mathrm{8}} \theta\mathrm{sec}^{\mathrm{6}} \alpha,\:\frac{\mathrm{1}}{\mathrm{2}},\:\mathrm{sin}^{\mathrm{8}} \theta\mathrm{cosec}^{\mathrm{6}} \alpha \\ $$$$\mathrm{are}\:\mathrm{in}\:\mathrm{which}\:\mathrm{progression}? \\…
Question Number 143858 by gsk2684 last updated on 19/Jun/21 $$\mathrm{if}\:\mathrm{A}\geqslant\mathrm{0},\:\mathrm{B}\geqslant\mathrm{0},\:\mathrm{A}+\mathrm{B}=\frac{\Pi}{\mathrm{3}}\:\mathrm{then} \\ $$$$\mathrm{find}\:\mathrm{minimum}\:\mathrm{and}\:\mathrm{maximum}\: \\ $$$$\mathrm{of}\:\mathrm{tan}\:\mathrm{A}.\mathrm{tan}\:\mathrm{B}\: \\ $$ Answered by ajfour last updated on 19/Jun/21 $$\sqrt{\mathrm{3}}=\frac{{p}+{q}}{\mathrm{1}−{pq}} \\…