What is simplify-cos(2pin)+cos(pin) ?

The solution to simplify-cos(2pin)+cos(pin) is -1+(-1)^n

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simplify-cos(2pin)+cos(pin)

simplify

- cos (2 πn) + cos (πn)

- 1 + (- 1)^{n}

Solution steps

- cos (2 πn) + cos (πn)

Use the basic trigonometric identity:

cos (nπ) = (- 1)^{n}

= - cos (2 nπ) + (- 1)^{n}

Use the Double Angle identity:

cos (2 x) = 1 - 2 sin^{2} (x)

= 1 - 2 sin^{2} (πn)

Simplify

1 - 2 sin^{2} (πn) : 1

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

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

49 (1 - sin^{2} (θ))

cos (6 0^{\circ} + X)

cot (\frac{π}{2} - u)

4 - 4 cos^{2} (t)

What is simplify-cos(2pin)+cos(pin) ?
The solution to simplify-cos(2pin)+cos(pin) is -1+(-1)^n