Determine if True cos(pi/4)cos(pi/6)=1/2(cos(pi/12)+cos((5pi)/12))

$\cos (\frac{π}{4}) \cos (\frac{π}{6}) = \frac{1}{2} (\cos (\frac{π}{12}) + \cos (\frac{5 π}{12}))$

Simplify $\frac{\sqrt{6} + \sqrt{2}}{8} + \frac{\sqrt{6} - \sqrt{2}}{8}$ .

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Combine the numerators over the common denominator.

$\frac{\sqrt{6}}{4} = \frac{\sqrt{6} + \sqrt{2} + \sqrt{6} - \sqrt{2}}{8}$

Simplify the numerator.

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Add $\sqrt{6}$ and $\sqrt{6}$ .

$\frac{\sqrt{6}}{4} = \frac{2 \sqrt{6} + \sqrt{2} - \sqrt{2}}{8}$

Subtract $\sqrt{2}$ from $\sqrt{2}$ .

$\frac{\sqrt{6}}{4} = \frac{2 \sqrt{6} + 0}{8}$

Add $2 \sqrt{6}$ and $0$ .

$\frac{\sqrt{6}}{4} = \frac{2 \sqrt{6}}{8}$

Cancel the common factor of $2$ and $8$ .

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Factor $2$ out of $2 \sqrt{6}$ .

$\frac{\sqrt{6}}{4} = \frac{2 (\sqrt{6})}{8}$

Cancel the common factors.

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Factor $2$ out of $8$ .

$\frac{\sqrt{6}}{4} = \frac{2 \sqrt{6}}{2 \cdot 4}$

Cancel the common factor.

$\frac{\sqrt{6}}{4} = \frac{2 \sqrt{6}}{2 \cdot 4}$

Rewrite the expression.

$\frac{\sqrt{6}}{4} = \frac{\sqrt{6}}{4}$

The left side $0.61237243$ is equal to the right side $0.61237243$ , which means that the given statement is always true.

True

Determine if True cos(pi/4)cos(pi/6)=1/2(cos(pi/12)+cos((5pi)/12))

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