What is expand-cos((1-n)pi+1) ?

The solution to expand-cos((1-n)pi+1) is cos(1)(-1)^{-n}

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expand-cos((1-n)pi+1)

expand

- cos ((1 - n) π + 1)

cos (1) (- 1)^{- n}

Solution steps

- cos ((1 - n) π + 1)

Expand

(1 - n) π + 1 : π - πn + 1

= - cos (π - πn + 1)

Use the basic trigonometric identity:

cos (x + nπ) = (- 1)^{n} cos (x)

= - (- 1)^{- n} cos (1 + π)

Rewrite using trig identities

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

Apply rule

- (- a) = a

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

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What is expand-cos((1-n)pi+1) ?
The solution to expand-cos((1-n)pi+1) is cos(1)(-1)^{-n}