What is expand sin((2n-1) pi/4) ?

The solution to expand sin((2n-1) pi/4) is (sin((pin)/2))/(sqrt(2))-(cos((pin)/2))/(sqrt(2))

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expand sin((2n-1) pi/4)

expand

sin ((2 n - 1) \frac{π}{4})

\frac{sin ( \frac{πn}{2} )}{2} - \frac{cos ( \frac{πn}{2} )}{2}

Solution steps

sin ((2 n - 1) \frac{π}{4})

Expand

(2 n - 1) \frac{π}{4} : \frac{πn}{2} - \frac{π}{4}

= sin (\frac{πn}{2} - \frac{π}{4})

Rewrite using trig identities

= \frac{2 sin ( \frac{πn}{2} ) - 2 cos ( \frac{πn}{2} )}{2}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{2 sin ( \frac{πn}{2} ) - 2 cos ( \frac{πn}{2} )}{2} = \frac{2 sin ( \frac{πn}{2} )}{2} - \frac{2 cos ( \frac{πn}{2} )}{2}

= \frac{2 sin ( \frac{πn}{2} )}{2} - \frac{2 cos ( \frac{πn}{2} )}{2}

Cancel

\frac{2 sin ( \frac{πn}{2} )}{2} : \frac{sin ( \frac{πn}{2} )}{2}

= \frac{sin ( \frac{πn}{2} )}{2} - \frac{2 cos ( \frac{πn}{2} )}{2}

Cancel

\frac{2 cos ( \frac{πn}{2} )}{2} : \frac{cos ( \frac{πn}{2} )}{2}

= \frac{sin ( \frac{πn}{2} )}{2} - \frac{cos ( \frac{πn}{2} )}{2}

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What is expand sin((2n-1) pi/4) ?
The solution to expand sin((2n-1) pi/4) is (sin((pin)/2))/(sqrt(2))-(cos((pin)/2))/(sqrt(2))