Question

Cos 60°×cos45° + sin 45°×sin 30°​

Answer 1

Answer:

0.707106781

Step-by-step explanation:

This is the right answer

Answer 2

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Cos 60°×cos45° + sin 45°×sin 30°​

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$\begin{gathered} cos45 \degree cos60 \degree-sin45 \degree sin60 \degree\\=\frac{\sqrt{2}-\sqrt{6}}{4}\end{gathered} cos45°cos60°−sin45°sin60°= 42​ − 6$

Step-by-step explanation:

$cos45\degree cos60\degree-sin45\degree sin60\degreecos45°cos60°−sin45°sin60°$

$=\frac{1}{\sqrt{2}}\times \frac{1}{2}-\frac{1}{\sqrt{2}}\times \frac{\sqrt{3}}{2}= 2​ 1​ × 21​ − 2​ 1​ × 23$               $\begin{gathered}=\frac{1}{2\sqrt{2}}-\frac{\sqrt{3}}{2\sqrt{2}}\\=\frac{1-\sqrt{3}}{2\sqrt{2}}\\=\frac{\sqrt{2}(1-\sqrt{3})}{2\sqrt{2}\times \sqrt{2}}\\=\frac{\sqrt{2}-\sqrt{6}}{4}\end{gathered} = 2 2​ 1​ − 2 2​ 3​ ​ = 2 2​ 1− 3​ ​ = 2 2​ × 2​ 2​ (1− 3​ )​ = 42​ − 6$

Therefore,

$\begin{gathered} cos45\degree cos60\degree-sin45\degree sin60\degree\\=\frac{\sqrt{2}-\sqrt{6}}{4}\end{gathered} cos45°cos60°−sin45°sin60°= 42​ −$

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Thanks!

Gummie!