Question

найти cos2α, если sinα=-1/4

Answer 1

$\cos^2 \alpha + \sin^2 \alpha=1 \\ \\ \cos^2 \alpha =1 -\sin^2 \alpha \\ \\ \cos^2 \alpha =1 - (-\frac{1}{4})^2=1 - \frac{1}{16} =\frac{15}{16} \\ \\ \cos2\alpha = \cos^2 \alpha - \sin^2 \alpha = (\frac{15}{16}- (-\frac{1}{4})^2)=\frac{15}{16}-\frac{1}{16}=\frac{14}{16}=\frac{7}{8}$

Answer 2

$cos2 \alpha =1-2sin^2 \alpha$
$cos2 \alpha =1-2*(- \frac{1}{4} )^2=1-2* \frac{1}{16} =1- \frac{1}{8} = \frac{7}{8}$