Obliczenia :
[tex]\sin\alpha=\frac{2}{5}\\\\\sin^2\alpha+\cos^2\alpha=1\\\\(\frac{2}{5})^2+\cos^2\alpha=1\\\\\frac{4}{25}+\cos^2\alpha=1 \ \ |-\frac{4}{25}\\\\\cos^2\alpha=\frac{21}{25}\\\\2\sin^2\alpha+5\cos^2\alpha=2\cdot\frac{4}{25}+5\cdot\frac{21}{25}=\\\\=\frac{8}{25}+\frac{21}{5}=0,32+4,2=\boxed{4,52}[/tex]
Odp. 2sin²α + 5cos²α = 4,52.
