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Category: Trigonometry

Question-108780

Question Number 108780 by 150505R last updated on 19/Aug/20 Answered by bobhans last updated on 19/Aug/20 $$\mathrm{cot}\:^{\mathrm{2}} \:\mathrm{81}°\:=\:\mathrm{tan}\:^{\mathrm{2}} \:\mathrm{9}\: \\ $$$$\mathrm{cot}\:^{\mathrm{2}} \:\mathrm{63}°\:=\:\mathrm{tan}\:^{\mathrm{2}} \:\mathrm{27}\: \\ $$$$\left(\ast\right)\:\frac{\mathrm{1}}{\mathrm{2}−\mathrm{cot}\:^{\mathrm{2}}…

Question-43192

Question Number 43192 by Raj Singh last updated on 08/Sep/18 Commented by Rauny last updated on 09/Sep/18 $$\mathrm{cosec}\:{x}+\mathrm{sec}\:{x}=\frac{\mathrm{1}}{\mathrm{sin}\:{x}}+\frac{\mathrm{1}}{\mathrm{cos}\:{x}}=\mathrm{2} \\ $$$$\mathrm{cos}\:{x}+\mathrm{sin}\:{x}=\mathrm{2sin}\:{x}\mathrm{cos}\:{x} \\ $$$${A}={B}\Rightarrow{A}^{\mathrm{2}} ={B}^{\mathrm{2}} , \\…

bemath-find-the-value-of-sin-pi-9-sin-2pi-9-sin-3pi-9-sin-4pi-9-

Question Number 108644 by bemath last updated on 18/Aug/20 $$\:\:\:\frac{{bemath}}{\bigstar} \\ $$$${find}\:{the}\:{value}\:{of}\: \\ $$$$\mathrm{sin}\:\left(\frac{\pi}{\mathrm{9}}\right)\mathrm{sin}\:\left(\frac{\mathrm{2}\pi}{\mathrm{9}}\right)\mathrm{sin}\:\left(\frac{\mathrm{3}\pi}{\mathrm{9}}\right)\mathrm{sin}\:\left(\frac{\mathrm{4}\pi}{\mathrm{9}}\right)?\: \\ $$ Commented by bemath last updated on 18/Aug/20 $${great}\:{answer}\:{all}\:{master} \\…

in-AB-C-prove-cos-A-a-3-cos-B-b-3-cos-C-c-3-81-16p-3-where-p-a-b-c-2-

Question Number 173983 by mnjuly1970 last updated on 23/Jul/22 $$ \\ $$$$\:\:\:{in}\:{A}\overset{\Delta} {{B}C}\:\:{prove}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\frac{\:{cos}\left({A}\:\right)}{{a}^{\:\mathrm{3}} }\:+\frac{{cos}\left({B}\right)}{{b}^{\:\mathrm{3}} }\:+\frac{{cos}\left({C}\right)}{{c}^{\:\mathrm{3}} }\:\geqslant\frac{\mathrm{81}}{\mathrm{16}{p}^{\:\mathrm{3}} } \\ $$$$\:\:\:{where}\::\:\:{p}=\:\left({a}+{b}\:+{c}\:\right)/\mathrm{2} \\ $$$$…

if-x-sinx-than-prove-that-x-4-x-2-1-

Question Number 173893 by azadsir last updated on 20/Jul/22 $$\mathrm{if}\:\int\left(\mathrm{x}\right)\:=\:\mathrm{sinx}\:\mathrm{than}\:\mathrm{prove}\:\mathrm{that}, \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\left\{\int\left(\mathrm{x}\right)^{\mathrm{4}} \right\}\:+\:\left\{\int\left(\mathrm{x}\right)\right\}^{\mathrm{2}} \:=\:\mathrm{1} \\ $$ Commented by MJS_new last updated on 20/Jul/22 $$\int\:\mathrm{is}\:\mathrm{the}\:\mathrm{integral}\:\mathrm{sign}… \\…