Question

sin 75 degree and Cos 75 degree​

Answer 1

Answer:

$sin75\degree=\frac{\sqrt{3}+1}{2\sqrt{2}}$

$cos75\degree=\frac{\sqrt{3}-1}{2\sqrt{2}}$

Step-by-step explanation:

$sin75\degree\\=sin(45+30)\\=sin45cos30+sin30cos45\\=\frac{1}{\sqrt{2}}\times \frac{\sqrt{3}}{2}+\frac{1}{2}\times \frac{1}{\sqrt{2}}\\=\frac{\sqrt{3}}{2\sqrt{2}}+\frac{1}{2\sqrt{2}}\\=\frac{\sqrt{3}+1}{2\sqrt{2}}$

$cos75\degree\\=cos(45+30)\\=cos45cos30-sin30cos45\\=\frac{1}{\sqrt{2}}\times \frac{\sqrt{3}}{2}-\frac{1}{2}\times \frac{1}{\sqrt{2}}\\=\frac{\sqrt{3}}{2\sqrt{2}}-\frac{1}{2\sqrt{2}}\\=\frac{\sqrt{3}-1}{2\sqrt{2}}$

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