What is isin((2n-1)*pi/2) ?

The solution to isin((2n-1)*pi/2) is -(-1)^ni

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simplify isin((2n-1)*pi/2)

simplify

i sin ((2 n - 1) \cdot \frac{π}{2})

- (- 1)^{n} i

Solution steps

i sin ((2 n - 1) \frac{π}{2})

Expand

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

= i sin (πn - \frac{π}{2})

Rewrite using trig identities

= i (- cos (πn))

Remove parentheses:

(- a) = - a

= - i cos (πn)

Use the basic trigonometric identity:

cos (nπ) = (- 1)^{n}

= - i (- 1)^{n}

cos (t - π) - sin (t - π)

sec (- t) - cos (- t) tan^{2} (- t)

cos (2 π + nπ)

cos (\frac{nπ}{2} - \frac{π}{2})

sin (- sin (x))