What is the value of cos((5pi)/(12))-cos(pi/(12)) ?

The value of cos((5pi)/(12))-cos(pi/(12)) is -(sqrt(2))/2

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cos((5pi)/(12))-cos(pi/(12))

cos (\frac{5 π}{12}) - cos (\frac{π}{12})

- \frac{2}{2}

Solution steps

cos (\frac{5 π}{12}) - cos (\frac{π}{12})

Rewrite using trig identities:

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

= - 2 sin (\frac{π}{4}) sin (\frac{π}{6})

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

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

Simplify

- 2 \cdot \frac{2}{2} \cdot \frac{1}{2} : - \frac{2}{2}

= - \frac{2}{2}

csc (\frac{5 π}{12})

tan (4 5^{\circ} + 3 0^{\circ})

tan (9 1^{\circ})

arctan (\frac{2}{- 2})

ln (cos (\frac{π}{2}))

What is the value of cos((5pi)/(12))-cos(pi/(12)) ?
The value of cos((5pi)/(12))-cos(pi/(12)) is -(sqrt(2))/2