The pythagorean identity 1 cot2 t csc2 t relates the

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Unformatted text preview: )), and the reader is encouraged to fill in the details. Below we summarize all of the sum and difference formulas for cosine, sine and tangent. Theorem 10.16. Sum and Difference Identities: For all applicable angles α and β , • cos(α ± β ) = cos(α) cos(β ) sin(α) sin(β ) • sin(α ± β ) = sin(α) cos(β ) ± cos(α) sin(β ) • tan(α ± β ) = tan(α) ± tan(β ) 1 tan(α) tan(β ) In the statement of Theorem 10.16, we have combined the cases for the sum ‘+’ and difference ‘−’ of angles into one formula. The convention here is that if you want the formula for the sum ‘+’ of 10.4 Trigonometric Identities 661 two angles, you use the top sign in the formula; for the difference, ‘−’, use the bottom sign. For example, tan(α) − tan(β ) tan(α − β ) = 1 + tan(α) tan(β ) If we specialize the sum formulas in Theorem 10.16 to the case when α = β , we obtain the following ‘Double Angle’ Identities. Theorem 10.17. Double Angle Identities: For all angles θ, 2 2 cos (θ) − sin (θ) 2 cos2 (θ) − 1 • cos(2θ)...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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