Odpowiedź:
[tex]\boxed{cos^{2}15^{0}+cos^{2}30^{0} + cos^{2}45^{0} + cos^{2}60^{0} + cos^{2}75^{0} = 2\frac{1}{2}}[/tex]
Szczegółowe wyjaśnienie:
[tex]sin^{2}\alpha + cos^{2}\alpha = 1\\\\cos^{2}15^{0} = cos^{2}(90^{0}-75^{0}) =sin^{2}15^{0}\\\\cos30^{0} = \frac{\sqrt{3}}{2}\\\\cos45^{0} = \frac{\sqrt{2}}{2}\\\\cos60^{0} = \frac{1}{2}[/tex]
[tex]cos^{2}15^{0} + cos^{2}30^{0} + cos^{2}45^{0} + cos^{2}60^{0} + cos^{2}75^{0} =\\\\=cos^{2}(90^{0}-75^{0}) +(\frac{\sqrt{3}}{2})^{2} + (\frac{\sqrt{2}}{2})^{2} + (\frac{1}{2}) ^{2} + cos^{2}75^{0}=\\\\=sin^{2}75^{2}+cos^{2}75^{0} + \frac{3}{4}+\frac{2}{4}+\frac{1}{4}=\\\\=1+\frac{6}{4} = 1+1\frac{2}{4} = 2\frac{2}{4} = \boxed{2\frac{1}{2}}[/tex]