sin-cos-3-8-3-sin-cos-

Question Number 149468 by mathdanisur last updated on 05/Aug/21

$${sin}\boldsymbol{\alpha}\:\centerdot\:{cos}\boldsymbol{\alpha}\:=\:\frac{\mathrm{3}}{\mathrm{8}}\:\Rightarrow\:\mathrm{3}\mid{sin}\boldsymbol{\alpha}\:-\:{cos}\boldsymbol{\alpha}\mid=? \\ $$

Answered by Olaf_Thorendsen last updated on 05/Aug/21

Let x = 3∣sinα−cosα∣ x^2 = 9(sin^2 +cos^2 α−2sinα.cosα) x^2 = 9(1−2×(3/8)) = (9/4) x = (3/2)

$$\mathrm{Let}\:{x}\:=\:\mathrm{3}\mid\mathrm{sin}\alpha−\mathrm{cos}\alpha\mid \\ $$$${x}^{\mathrm{2}} \:=\:\mathrm{9}\left(\mathrm{sin}^{\mathrm{2}} +\mathrm{cos}^{\mathrm{2}} \alpha−\mathrm{2sin}\alpha.\mathrm{cos}\alpha\right) \\ $$$${x}^{\mathrm{2}} \:=\:\mathrm{9}\left(\mathrm{1}−\mathrm{2}×\frac{\mathrm{3}}{\mathrm{8}}\right)\:=\:\frac{\mathrm{9}}{\mathrm{4}} \\ $$$${x}\:=\:\frac{\mathrm{3}}{\mathrm{2}} \\ $$

Commented by mathdanisur last updated on 05/Aug/21