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

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

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sin(pi/(12))-sin((5pi)/(12))

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

- \frac{2}{2}

Solution steps

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

Rewrite using trig identities:

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

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

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

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

Simplify

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

= - \frac{2}{2}

arcsin (\frac{1}{2}) + arcsin (\frac{3}{2})

csc (arccos (\frac{21}{7}))

cos (2 \frac{3 π}{4})

- ln ∣ cos (0) ∣

tan (- \frac{7 π}{2})

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