What is the value of cos(pi/4+pi/6) ?

The value of cos(pi/4+pi/6) is (sqrt(6)-sqrt(2))/4

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cos(pi/4+pi/6)

cos (\frac{π}{4} + \frac{π}{6})

\frac{6 - 2}{4}

Solution steps

cos (\frac{π}{4} + \frac{π}{6})

Rewrite using trig identities:

cos (\frac{π}{4}) cos (\frac{π}{6}) - sin (\frac{π}{4}) sin (\frac{π}{6})

= cos (\frac{π}{4}) cos (\frac{π}{6}) - sin (\frac{π}{4}) sin (\frac{π}{6})

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

= \frac{2}{2} \cdot \frac{3}{2} - \frac{2}{2} \cdot \frac{1}{2}

Simplify

\frac{2}{2} \cdot \frac{3}{2} - \frac{2}{2} \cdot \frac{1}{2} : \frac{6 - 2}{4}

= \frac{6 - 2}{4}

tan (\frac{4}{3})

2 sin (3 0^{\circ}) cos (3 0^{\circ})

arctan (\frac{4}{2})

sin (11 0^{\circ})

arctan (\frac{8}{5})

What is the value of cos(pi/4+pi/6) ?
The value of cos(pi/4+pi/6) is (sqrt(6)-sqrt(2))/4