Menu Close

show-that-sin-2-1-cos-2-2-1-cos-




Question Number 172026 by Mikenice last updated on 23/Jun/22
show that  sin^2 α+(1+cosα)^2 =2(1+cosα)
$${show}\:{that} \\ $$$${sin}^{\mathrm{2}} \alpha+\left(\mathrm{1}+{cos}\alpha\right)^{\mathrm{2}} =\mathrm{2}\left(\mathrm{1}+{cos}\alpha\right) \\ $$
Answered by puissant last updated on 23/Jun/22
sin^2 α+(1+cosα)^2   = sin^2 α + 1 +2cosα+cos^2 α  = sin^2 α+cos^2 α+1+2cosα  =2+2cosα  =2(1+cosα)
$${sin}^{\mathrm{2}} \alpha+\left(\mathrm{1}+{cos}\alpha\right)^{\mathrm{2}} \\ $$$$=\:{sin}^{\mathrm{2}} \alpha\:+\:\mathrm{1}\:+\mathrm{2}{cos}\alpha+{cos}^{\mathrm{2}} \alpha \\ $$$$=\:{sin}^{\mathrm{2}} \alpha+{cos}^{\mathrm{2}} \alpha+\mathrm{1}+\mathrm{2}{cos}\alpha \\ $$$$=\mathrm{2}+\mathrm{2}{cos}\alpha \\ $$$$=\mathrm{2}\left(\mathrm{1}+{cos}\alpha\right) \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *