What is simplify-cos(npi)-cos(pi) ?

The solution to simplify-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}

Apply rule

- (- a) = a

= 1 - (- 1)^{n}

tan (3 0^{\circ} - x)

tan (- 3 x^{5})

csc (180 0^{\circ} - α)

sin (x) sin (18 0^{\circ} - x)

x ln (cos (\frac{π}{2} - x))

What is simplify-cos(npi)-cos(pi) ?
The solution to simplify-cos(npi)-cos(pi) is 1-(-1)^n