Question

cos45°*cos60°-sin45°*sin60°

Answer 1

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Answer 2

Answer:

$cos45 \degree cos60 \degree-sin45 \degree sin60 \degree\\=\frac{\sqrt{2}-\sqrt{6}}{4}$

Step-by-step explanation:

$cos45\degree cos60\degree-sin45\degree sin60\degree$

$=\frac{1}{\sqrt{2}}\times \frac{1}{2}-\frac{1}{\sqrt{2}}\times \frac{\sqrt{3}}{2}$$=\frac{1}{2\sqrt{2}}-\frac{\sqrt{3}}{2\sqrt{2}}\\=\frac{1-\sqrt{3}}{2\sqrt{2}}\\=\frac{\sqrt{2}(1-\sqrt{3})}{2\sqrt{2}\times \sqrt{2}}\\=\frac{\sqrt{2}-\sqrt{6}}{4}$

Therefore,

$cos45\degree cos60\degree-sin45\degree sin60\degree\\=\frac{\sqrt{2}-\sqrt{6}}{4}$

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