Cho sin apha = 0,5 cos alpha. Tìm giá trị sin alpha, cos apha

Ta có: sin²α + cos²α = 1

⇔ (0,5cosα)² + cos²α = 1

⇔ 1,25 cos²α = 1

⇔ cos²α = \(\frac{4}{5}\)

⇔\[\left[ \begin{array}{l}\cos \alpha = \frac{2}{{\sqrt 5 }}\\\cos \alpha = - \frac{2}{{\sqrt 5 }}\end{array} \right.\]

⇔\[\left[ \begin{array}{l}\sin \alpha = \frac{1}{{\sqrt 5 }}\\\sin \alpha = - \frac{1}{{\sqrt 5 }}\end{array} \right.\].