What is the value of sin((7pi)/8)-sin((7pi)/6)-cot(pi/3) ?

The value of sin((7pi)/8)-sin((7pi)/6)-cot(pi/3) is 1/2+(3sqrt(-\sqrt{2)+2}-2sqrt(3))/6

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sin((7pi)/8)-sin((7pi)/6)-cot(pi/3)

sin (\frac{7 π}{8}) - sin (\frac{7 π}{6}) - cot (\frac{π}{3})

\frac{1}{2} + \frac{3 - 2 + 2 - 2 3}{6}

Solution steps

sin (\frac{7 π}{8}) - sin (\frac{7 π}{6}) - cot (\frac{π}{3})

Rewrite using trig identities:

sin (\frac{7 π}{8}) = \frac{2 - 2}{2}

Rewrite using trig identities:

sin (\frac{7 π}{6}) = - \frac{1}{2}

Use the following trivial identity:

cot (\frac{π}{3}) = \frac{3}{3}

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

Simplify

\frac{2 - 2}{2} - (- \frac{1}{2}) - \frac{3}{3} : \frac{1}{2} + \frac{3 - 2 + 2 - 2 3}{6}

= \frac{1}{2} + \frac{3 - 2 + 2 - 2 3}{6}

2 sin (6 0^{\circ}) sec (3 0^{\circ}) cos (4 5^{\circ}) tan (4 5^{\circ})

3 + 2 sin (\frac{π}{4})

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

arctan (\frac{2.5}{1.8})

7 sin (4 0^{\circ})

What is the value of sin((7pi)/8)-sin((7pi)/6)-cot(pi/3) ?
The value of sin((7pi)/8)-sin((7pi)/6)-cot(pi/3) is 1/2+(3sqrt(-\sqrt{2)+2}-2sqrt(3))/6