What is cos((1+n/2)*2pi) ?

The solution to cos((1+n/2)*2pi) is (-1)^n

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simplify cos((1+n/2)*2pi)

simplify

cos ((1 + \frac{n}{2}) \cdot 2 π)

(- 1)^{n}

Solution steps

cos ((1 + \frac{n}{2}) \cdot 2 π)

Expand

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

= cos (2 π + πn)

Rewrite using trig identities

= cos (πn)

Use the basic trigonometric identity:

cos (nπ) = (- 1)^{n}

= (- 1)^{n}

2 cos (x - \frac{2 π}{3})

r cos (θ - \frac{π}{6})

sin (t - \frac{1}{4} π)

sin (π t) \cdot sec (π t)

cos (arccos (v))