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If m, n integers and x = cos alpha + i ...

If m, n integers and ` x = cos alpha + i sin alpha , y = cos beta + i sin beta, ` then prove that ` x^(m) y^(n) + 1/(x^(m)y^(n)) = 2 cos ( m alpha + n beta) " and " x^(m) y^(n) - 1/(x^(m) y^(n)) = 2 i sin ( m alpha + n beta)`.

Text Solution

Verified by Experts

The correct Answer is:
`therefore x^m.y^n+(1)/(x^m.y^n)=cis (m alpha +n beta)+cis(m alpha-n beta)`
`=2cos(m alpha+n beta)`
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