Can you explain how to use the sum and difference formulas for sine, cosine, and tangent to solve complex trigonometric expressions?
Answer 1
Brandon Taylor
The sum and difference formulas for sine, cosine, and tangent are vital tools in trigonometry. They allow us to simplify complex expressions by breaking them into manageable parts. For sine: sin(a ± b) = sin(a)cos(b) ± cos(a)sin(b). For cosine: cos(a ± b) = cos(a)cos(b) ∓ sin(a)sin(b). For tangent: tan(a ± b) = (tan(a) ± tan(b)) / (1 ∓ tan(a)tan(b)). These formulas are particularly useful in solving equations, proving identities, and evaluating trigonometric functions at specific angles.
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