Oblicz:
a)
b)
c)
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a)![2(cos60+sin30)=2(\frac{1}{2}+\frac{1}{2})=2\\ sin^{2}45-cos^{2}60=(\frac{\sqrt2}{2})^2-(\frac{1}{2})^2=\frac{2}{4}-\frac{1}{4}=\frac{1}{4}\\\\\\ \frac{sin^{2}45+cos^{2}30}{tg45+1}=\frac{(\frac{\sqrt2}{2})^2+(\frac{\sqrt3}{2})^2}{1+1}=\frac{\frac{2}{4}+\frac{3}{4}}{2}=\frac{\frac{5}{4}}{2}=\frac{5}{8} 2(cos60+sin30)=2(\frac{1}{2}+\frac{1}{2})=2\\ sin^{2}45-cos^{2}60=(\frac{\sqrt2}{2})^2-(\frac{1}{2})^2=\frac{2}{4}-\frac{1}{4}=\frac{1}{4}\\\\\\ \frac{sin^{2}45+cos^{2}30}{tg45+1}=\frac{(\frac{\sqrt2}{2})^2+(\frac{\sqrt3}{2})^2}{1+1}=\frac{\frac{2}{4}+\frac{3}{4}}{2}=\frac{\frac{5}{4}}{2}=\frac{5}{8}](https://tex.z-dn.net/?f=2%28cos60%2Bsin30%29%3D2%28%5Cfrac%7B1%7D%7B2%7D%2B%5Cfrac%7B1%7D%7B2%7D%29%3D2%5C%5C+sin%5E%7B2%7D45-cos%5E%7B2%7D60%3D%28%5Cfrac%7B%5Csqrt2%7D%7B2%7D%29%5E2-%28%5Cfrac%7B1%7D%7B2%7D%29%5E2%3D%5Cfrac%7B2%7D%7B4%7D-%5Cfrac%7B1%7D%7B4%7D%3D%5Cfrac%7B1%7D%7B4%7D%5C%5C%5C%5C%5C%5C+%5Cfrac%7Bsin%5E%7B2%7D45%2Bcos%5E%7B2%7D30%7D%7Btg45%2B1%7D%3D%5Cfrac%7B%28%5Cfrac%7B%5Csqrt2%7D%7B2%7D%29%5E2%2B%28%5Cfrac%7B%5Csqrt3%7D%7B2%7D%29%5E2%7D%7B1%2B1%7D%3D%5Cfrac%7B%5Cfrac%7B2%7D%7B4%7D%2B%5Cfrac%7B3%7D%7B4%7D%7D%7B2%7D%3D%5Cfrac%7B%5Cfrac%7B5%7D%7B4%7D%7D%7B2%7D%3D%5Cfrac%7B5%7D%7B8%7D)