Oblicz

[Eqauzm]

Korzystając ze wzoru \(\displaystyle{ \cos(90^{0} - ) = \sin }\) , oblicz:


\(\displaystyle{ \cos ^{2} 25 ^{0} + \cos ^{2} 35 ^{0} + \cos ^{2} 45 ^{0} + \cos ^{2} 55 ^{0} + \cos ^{2} 65 ^{0}}\)

[mostostalek]

\(\displaystyle{ \cos ^{2} 25 ^{o} + \cos ^{2} 35 ^{o} + \cos ^{2} 45 ^{o} + \cos ^{2} 55 ^{o} + \cos ^{2} 65 ^{o} =\sin^2 65^{o}+ \sin^{2} 55^{o}+cos^245^o+\cos^255^o+cos^265^o=2+(\frac{\sqrt{2}}{2})^2=2+\frac{1}{2}=\frac{5}{2}}\)