Resposta :
Resposta:
Explicação passo a passo:
[tex]Passo\ 1\\\\sen(75\º)=sen(30\º+45\º)\\sen(75\º)=sen(30\º)*cos(45\º)+sen(45\º)*cos(30\º)\\sen(75\º)=\frac{1}{2}*\frac{\sqrt{2} }{2}+\frac{\sqrt{2} }{2}*\frac{\sqrt{3} }{2}\\sen(75\º)=\frac{\sqrt{2}+\sqrt{6} }{4}\\[/tex]
[tex]Passo\ 2\\\\sen^{2}(x)+cos^{2}(x)=1\\sen^{2}(75\º)+cos^{2}(75\º)=1\\(\frac{\sqrt{2}+\sqrt{6} }{4} )^{2}+cos^{2}(75\º)=1\\(\frac{2+4\sqrt{3}+6 }{16} ) +cos^{2}(75\º)=1\\cos^{2}(75\º)=1-\frac{8+4\sqrt{3} }{16}\\cos^{2}(75\º)=1-\frac{2+\sqrt{3} }{4}\\cos^{2}(75\º)=\frac{2-\sqrt{3} }{4}\\cos(75\º)=\sqrt{\frac{2-\sqrt{3} }{4}}[/tex]
[tex]Passo\ 3\\\\sen(75\º-x)=sen(75\º)*cos(x)+sen(x)*cos(75\º)\\sen(75\º-x)=(\frac{\sqrt{2}+\sqrt{6} }{4} )*cos(x)+sen(x)*\sqrt{\frac{2-\sqrt{3} }{4} }[/tex]