How do you derive the double-angle formulas for sine, cosine, and tangent from the basic trigonometric identities?
Answer 1
Michelle Gibson
To derive the double-angle formulas, we use the sum identities. For sine: sin(2θ) = 2sin(θ)cos(θ). For cosine: cos(2θ) = cos²(θ) – sin²(θ). For tangent: tan(2θ) = 2tan(θ) / (1 – tan²(θ)). These follow from the sum identities sin(a + b), cos(a + b), and tan(a + b).
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