What is the value of cos((7pi)/(12)) ?

The value of cos((7pi)/(12)) is (sqrt(2)(1-sqrt(3)))/4

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cos((7pi)/(12))

cos (\frac{7 π}{12})

\frac{2 ( 1 - 3 )}{4}

Solution steps

cos (\frac{7 π}{12})

Rewrite using trig identities:

cos (\frac{π}{3}) cos (\frac{π}{4}) - sin (\frac{π}{3}) sin (\frac{π}{4})

= cos (\frac{π}{3}) cos (\frac{π}{4}) - sin (\frac{π}{3}) sin (\frac{π}{4})

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

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

Simplify

\frac{1}{2} \cdot \frac{2}{2} - \frac{3}{2} \cdot \frac{2}{2} : \frac{2 ( 1 - 3 )}{4}

= \frac{2 ( 1 - 3 )}{4}

cos (\frac{7 π}{8})

cot (\frac{7 π}{6})

2 sin^{2} (θ) = 1

cos (x) = 0.5

sin (\frac{3}{2})

What is the value of cos((7pi)/(12)) ?
The value of cos((7pi)/(12)) is (sqrt(2)(1-sqrt(3)))/4