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Question Number 148445 by mathdanisur last updated on 28/Jul/21

if cos𝛂 = (√a) find 5 - 6cos2𝛂 + cos4𝛂 = ?

$${if}\:\:\:{cos}\boldsymbol{\alpha}\:=\:\sqrt{\boldsymbol{{a}}} \\ $$$${find}\:\:\:\mathrm{5}\:-\:\mathrm{6}{cos}\mathrm{2}\boldsymbol{\alpha}\:+\:{cos}\mathrm{4}\boldsymbol{\alpha}\:=\:? \\ $$

Commented by mathdanisur last updated on 28/Jul/21

Thank you Ser But, =(βˆšπ›‚) (alfa no) =(√a)

$${Thank}\:{you}\:{Ser} \\ $$$${But},\:=\sqrt{\boldsymbol{\alpha}}\:\left({alfa}\:{no}\right)\:\:=\sqrt{\boldsymbol{{a}}} \\ $$

Commented by mathdanisur last updated on 28/Jul/21

answer: a)8a^2 -20a+12 b)8a^2 +18a-12 c)2a-1 d)8a^2 -8a+1 e)1-5a

$$\left.{a}\left.{nswer}:\:{a}\right)\mathrm{8}{a}^{\mathrm{2}} -\mathrm{20}{a}+\mathrm{12}\:\:{b}\right)\mathrm{8}{a}^{\mathrm{2}} +\mathrm{18}{a}-\mathrm{12} \\ $$$$\left.{c}\left.\right)\left.\mathrm{2}{a}-\mathrm{1}\:{d}\right)\mathrm{8}{a}^{\mathrm{2}} -\mathrm{8}{a}+\mathrm{1}\:{e}\right)\mathrm{1}-\mathrm{5}{a} \\ $$

Commented by Olaf_Thorendsen last updated on 28/Jul/21

you are right ! sorry mister. my eyes are very old.

$$\mathrm{you}\:\mathrm{are}\:\mathrm{right}\:! \\ $$$$\mathrm{sorry}\:\mathrm{mister}. \\ $$$$\mathrm{my}\:\mathrm{eyes}\:\mathrm{are}\:\mathrm{very}\:\mathrm{old}. \\ $$

Answered by Olaf_Thorendsen last updated on 28/Jul/21

x = 5βˆ’6cos2Ξ±+cos4Ξ± x = 5βˆ’6cos2Ξ±+2cos^2 2Ξ±βˆ’1 x = 2cos^2 2Ξ±βˆ’6cos2Ξ±+4 x = 2(2cos^2 Ξ±βˆ’1)^2 βˆ’6(2cos^2 Ξ±βˆ’1)+4 x = 2(2aβˆ’1)^2 βˆ’6(2aβˆ’1)+4 x = 8a^2 βˆ’20a+12

$${x}\:=\:\mathrm{5}βˆ’\mathrm{6cos2}\alpha+\mathrm{cos4}\alpha \\ $$$${x}\:=\:\mathrm{5}βˆ’\mathrm{6cos2}\alpha+\mathrm{2cos}^{\mathrm{2}} \mathrm{2}\alphaβˆ’\mathrm{1} \\ $$$${x}\:=\:\mathrm{2cos}^{\mathrm{2}} \mathrm{2}\alphaβˆ’\mathrm{6cos2}\alpha+\mathrm{4} \\ $$$${x}\:=\:\mathrm{2}\left(\mathrm{2cos}^{\mathrm{2}} \alphaβˆ’\mathrm{1}\right)^{\mathrm{2}} βˆ’\mathrm{6}\left(\mathrm{2cos}^{\mathrm{2}} \alphaβˆ’\mathrm{1}\right)+\mathrm{4} \\ $$$${x}\:=\:\mathrm{2}\left(\mathrm{2}{a}βˆ’\mathrm{1}\right)^{\mathrm{2}} βˆ’\mathrm{6}\left(\mathrm{2}{a}βˆ’\mathrm{1}\right)+\mathrm{4} \\ $$$${x}\:=\:\mathrm{8}{a}^{\mathrm{2}} βˆ’\mathrm{20}{a}+\mathrm{12} \\ $$

Commented by mathdanisur last updated on 28/Jul/21

Thank you very much Sir

$${Thank}\:{you}\:{very}\:{much}\:{Sir} \\ $$

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