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

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

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cos((7pi)/(12))-cos(pi/(12))

cos (\frac{7 π}{12}) - cos (\frac{π}{12})

- \frac{3}{2}

Solution steps

cos (\frac{7 π}{12}) - cos (\frac{π}{12})

Rewrite using trig identities:

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

= - 2 sin (\frac{π}{3}) sin (\frac{π}{4})

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

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

Simplify

- 2 \cdot \frac{3}{2} \cdot \frac{2}{2} : - \frac{3}{2}

= - \frac{3}{2}

sin (2 arccos (\frac{12}{13}))

cot (51 0^{\circ})

\frac{sin ( 1 )}{cos ( 1 )}

arctan (0.44)

arccos (\frac{1}{30})

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