Pre-Calc Exam Notes 73

Pre-Calc Exam Notes 73 - Sum and Difference Formulas...

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Sum and Difference Formulas Section 3.2 73 Using the identity tan θ = sin θ cos θ , and the addition formulas for sine and cosine, we can derive the addition formula for tangent: tan ( A + B ) = sin ( A + B ) cos ( A + B ) = sin A cos B + cos A sin B cos A cos B sin A sin B = sin A cos B cos A cos B + cos A sin B cos A cos B cos A cos B cos A cos B sin A sin B cos A cos B (divide top and bottom by cos A cos B ) = sin A cos A · a a a cos B cos B + a a a cos A cos A · sin B cos B 1 sin A cos A · sin B cos B = tan A + tan B 1 tan A tan B This, combined with replacing B by B and using the relation tan ( θ ) = − tan θ , gives us the addition and subtraction formulas for tangent: tan ( A + B ) = tan A + tan B 1 tan A tan B (3.18) tan ( A B ) = tan A tan B 1 + tan A tan B (3.19) Example 3.8 Given angles A and B such that sin A = 4 5 , cos A = 3 5 , sin B = 12 13 , and cos B = 5 13 , Fnd the exact values
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