What is the value of sin((11pi)/(12))-sin((7pi)/(12)) ?

The value of sin((11pi)/(12))-sin((7pi)/(12)) is -(sqrt(2))/2

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sin((11pi)/(12))-sin((7pi)/(12))

sin (\frac{11 π}{12}) - sin (\frac{7 π}{12})

- \frac{2}{2}

Solution steps

sin (\frac{11 π}{12}) - sin (\frac{7 π}{12})

Rewrite using trig identities:

2 sin (\frac{π}{6}) cos (\frac{3 π}{4})

= 2 sin (\frac{π}{6}) cos (\frac{3 π}{4})

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

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

Simplify

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

= - \frac{2}{2}

sin (2 arcsin (\frac{1}{2}))

tan (- \frac{13 π}{4})

- csc^{2} (\frac{3 π}{4})

arcsin (\frac{2}{π})

sin (69 0^{\circ})

What is the value of sin((11pi)/(12))-sin((7pi)/(12)) ?
The value of sin((11pi)/(12))-sin((7pi)/(12)) is -(sqrt(2))/2