Question

Prove that the family of trigonometric functions { 1, cos x, sin x, ..., cos nx,...

Prove that the family of trigonometric functions { 1, cos x, sin x, ..., cos nx, sin nx, ...} form an orthogonal system on [-pi,pi] prove that the following orthogonality relations

hold integral from -pi to pi of sin nx dx = 0 and integral from -pi to pi of cos nx dx = 0

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