What is cos(npi)+cos(pi) ?

The solution to cos(npi)+cos(pi) is -1+(-1)^n

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simplify cos(npi)+cos(pi)

simplify

cos (nπ) + cos (π)

- 1 + (- 1)^{n}

Solution steps

cos (nπ) + cos (π)

Use the basic trigonometric identity:

cos (nπ) = (- 1)^{n}

= cos (π) + (- 1)^{n}

Use the following trivial identity:

cos (π) = (- 1)

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= - 1 + (- 1)^{n}

cos (- \frac{π}{2} - x)

cos (- u)

sin (x - 3 π)

\frac{cos ( nπ )}{n}

5 csc^{2} (- 5 - 2 csc (x) + 2)