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4.3 Sum, Difference, and Cofunction Identities

4.3 Sum, Difference, and Cofunction Identities. Sum and difference identities for cosine Cofunction identities Sum and difference identities for sine and tangent Summary and use. Sum and Difference Identities for Cosine. cos(x – y) = cos x cos y - sin x sin y Claim: cos( p /2 – y) = siny

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4.3 Sum, Difference, and Cofunction Identities

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  1. 4.3 Sum, Difference, and Cofunction Identities • Sum and difference identities for cosine • Cofunction identities • Sum and difference identities for sine and tangent • Summary and use

  2. Sum and Difference Identities for Cosine • cos(x – y) = cos x cos y - sin x sin y • Claim: cos(p/2 – y) = siny • Proof: • cos(p/2 – y) = cos (p/2) cos y + sin(p/2) sin y = 0 cos y + 1 sin y = sin y

  3. Sum and Difference Formula for Sine and Tangent sin (x- y) = sin x cos x + cos x sin y

  4. Finding Exact Values • Find the exact value of cos 15º • Solution:

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