[tex]ctg45^{o} = 1\\sin60^{o} = \frac{\sqrt{3}}{2}\\cos30^{o} = \frac{\sqrt{3}}{2}\\tg45^{o} = 1[/tex]
[tex]4(ctg45^{o}+sin60^{o})(cos30^{o}+tg45^{o}) = 4(1+\frac{\sqrt{3}}{2})(\frac{\sqrt{3}}{2}+1) = 4(1+\frac{\sqrt{3}}{2})^{2} =\\\\=4(1^{2}+2\cdot1\cdot\frac{\sqrt{3}}{2}+(\frac{\sqrt{3}}{2})^{2}) = 4(1+\sqrt{3}+\frac{3}{4}) =4+4\sqrt{3}+3 = 7+4\sqrt{3}[/tex]
Wyjaśnienie:
[tex](a+b)^{2} = a^{2}+2ab + b^{2}[/tex]
