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Sum and Difference Formulas:There are four possible products of two factors that can be formed from , , , and . Namely: , , , . Note their distribution in the first four formulas. The right hand sides of (1) and (2) consist of the algebraic sum of and , while (3) and (4) consist of the mixed products. Note the distribution of signs below. In formulas 1 and 2, for cosine the signs on each side of the formulas are "opposite". Be aware of the order of the subtraction: the product of cosine minus the product of sine. In formulas 3 and 4, for sine the signs on both sides are the same. Be aware of the subtraction in formula 4: in front of the product is negative, when the product contains the factor , where is from the term of . Formulas 5 and 6, tangents have the same sign in the numerator of both sides. The numerator is also what you get if you multiply tangent by (i.e. . Notice, this is not actually how it works). The denominator is , the sign being the opposite of the numerator. |
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