Sum/Difference & Double Angle Formulas

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What is the formula for the tangent of the difference of two angles?

Back

The formula for the tangent of the difference of two angles is: tan(α - β) = \frac{tan(α) - tan(β)}{1 + tan(α)tan(β)}.

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What is the formula for the tangent of the sum of two angles?

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The formula for the tangent of the sum of two angles is: tan(α + β) = \frac{tan(α) + tan(β)}{1 - tan(α)tan(β)}.

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What is the double angle formula for sine?

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The double angle formula for sine is: sin(2u) = 2sin(u)cos(u).

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What is the double angle formula for cosine?

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The double angle formula for cosine is: cos(2u) = cos^2(u) - sin^2(u).

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What is the double angle formula for tangent?

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The double angle formula for tangent is: tan(2u) = \frac{2tan(u)}{1 - tan^2(u)}.

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What is the Pythagorean identity for sine and cosine?

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The Pythagorean identity states that: sin^2(x) + cos^2(x) = 1.

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How do you find sin(2θ) using the double angle formula?

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To find sin(2θ), use the formula: sin(2θ) = 2sin(θ)cos(θ).

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What is the value of sin(105°) using sum formulas?

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Using the sum formula, sin(105°) can be expressed as: sin(105°) = sin(60° + 45°) = sin(60°)cos(45°) + cos(60°)sin(45°) = \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{2}}{2} + \frac{1}{2} \cdot \frac{\sqrt{2}}{2} = \frac{\sqrt{6} + \sqrt{2}}{4}.

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What is the value of cos(2θ) using the double angle formula?

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Using the double angle formula, cos(2θ) can be expressed as: cos(2θ) = cos^2(θ) - sin^2(θ).

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What is the relationship between sin^2(x) and cos^2(x)?

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The relationship is given by the Pythagorean identity: sin^2(x) = 1 - cos^2(x).