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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, =(√𝛂) (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 = 5−6cos2α+cos4α  x = 5−6cos2α+2cos^2 2α−1  x = 2cos^2 2α−6cos2α+4  x = 2(2cos^2 α−1)^2 −6(2cos^2 α−1)+4  x = 2(2a−1)^2 −6(2a−1)+4  x = 8a^2 −20a+12
$${x}\:=\:\mathrm{5}−\mathrm{6cos2}\alpha+\mathrm{cos4}\alpha \\ $$$${x}\:=\:\mathrm{5}−\mathrm{6cos2}\alpha+\mathrm{2cos}^{\mathrm{2}} \mathrm{2}\alpha−\mathrm{1} \\ $$$${x}\:=\:\mathrm{2cos}^{\mathrm{2}} \mathrm{2}\alpha−\mathrm{6cos2}\alpha+\mathrm{4} \\ $$$${x}\:=\:\mathrm{2}\left(\mathrm{2cos}^{\mathrm{2}} \alpha−\mathrm{1}\right)^{\mathrm{2}} −\mathrm{6}\left(\mathrm{2cos}^{\mathrm{2}} \alpha−\mathrm{1}\right)+\mathrm{4} \\ $$$${x}\:=\:\mathrm{2}\left(\mathrm{2}{a}−\mathrm{1}\right)^{\mathrm{2}} −\mathrm{6}\left(\mathrm{2}{a}−\mathrm{1}\right)+\mathrm{4} \\ $$$${x}\:=\:\mathrm{8}{a}^{\mathrm{2}} −\mathrm{20}{a}+\mathrm{12} \\ $$
Commented by mathdanisur last updated on 28/Jul/21
Thank you very much Sir
$${Thank}\:{you}\:{very}\:{much}\:{Sir} \\ $$

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