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Question Number 84205 by 1406 last updated on 10/Mar/20 $${prove}\: \\ $$$${a}.\:{sin}\mathrm{2}{x}={tanx}\left(\mathrm{1}+{cos}\mathrm{2}{x}\right) \\ $$$${b}.\:{sin}\mathrm{2}{x}=\frac{\mathrm{2}{tanx}}{\mathrm{1}+{tan}^{\mathrm{2}} {x}} \\ $$ Answered by john santu last updated on 10/Mar/20…
Question Number 84206 by naka3546 last updated on 10/Mar/20 $${a},\:{b},\:{c},\:{d}\:\:\in\:\:\mathbb{N} \\ $$$$\left({a},\:{b},\:{c},\:{d}\right)\:\:{is}\:\:{quadruple}\:\:{of}\:\:{a},\:{b},\:{c},\:{d}\:\:{such}\:\:{that} \\ $$$$\:\:\:\:\:\:\:\:{b}\:\:=\:\:{a}^{\mathrm{2}} \:+\:\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:{c}\:\:=\:\:{b}^{\mathrm{2}} \:+\:\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:{d}\:\:=\:\:{c}^{\mathrm{2}} \:+\:\mathrm{1} \\ $$$$\tau\left({a}\right)\:+\:\tau\left({b}\right)\:+\:\tau\left({c}\right)\:+\:\tau\left({d}\right)\:\:{is}\:\:\:{odd}\:\:{number}\left({s}\right)\:. \\ $$$$\tau\left({k}\right)\:\:{is}\:\:{the}\:\:{number}\:\:{of}\:\:{positive}\:\:{divisor}\:\:{of}\:\:\:{natural}\:\:{number}\:\:{k}\:.…
Question Number 84202 by 1406 last updated on 10/Mar/20 $${prove}\: \\ $$$${cos}^{\mathrm{4}} {x}−{sin}^{\mathrm{4}} {x}={cos}\mathrm{22}{x} \\ $$ Answered by john santu last updated on 10/Mar/20 $$\left(\mathrm{cos}\:^{\mathrm{2}}…
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Question Number 84152 by naka3546 last updated on 09/Mar/20 Commented by MJS last updated on 09/Mar/20 $$\mathrm{we}\:\mathrm{have}\:\mathrm{to}\:\mathrm{find}\:\mathrm{for}\:\mathrm{which}\:\mathrm{values}\:\mathrm{of}\:{n}\:\mathrm{there} \\ $$$$\mathrm{is}\:\mathrm{such}\:\mathrm{an}\:{x}\:\mathrm{at}\:\mathrm{all}… \\ $$$$\mathrm{it}\:\mathrm{works}\:\mathrm{for}\:{n}=\mathrm{3}\:\mathrm{but}\:\mathrm{not}\:\mathrm{for}\:{n}=\mathrm{2}\:\mathrm{and}\:{n}=\mathrm{4} \\ $$$$… \\ $$…
Question Number 84156 by naka3546 last updated on 10/Mar/20 Commented by Tony Lin last updated on 10/Mar/20 Commented by Tony Lin last updated on 10/Mar/20…