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

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

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expand cos(pi(1+n))

expand

cos (π (1 + n))

- (- 1)^{n}

Solution steps

cos (π (1 + n))

Expand

π (1 + n) : π + πn

= cos (π + πn)

Rewrite using trig identities

= - cos (πn)

Use the basic trigonometric identity:

cos (nπ) = (- 1)^{n}

= - (- 1)^{n}

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