HSC Together Year 12 Maths Extension 1: Double Angle Formulae for Sine and Cosine

#### Maths Extension 1

• Proof
• Vectors
• Further Trigonometric Functions
• Further Calculus
• Further Statistical Analysis
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# Double Angle Formulae for Sine and Cosine

This topic is part of the HSC Mathematics Extension 1 syllabus under the topic Further Calculus.

In this post, we learn to prove and solve double angle formulae for sine and cosine.

Here are the formulae

Sine

sin(2x) = 2 sin(x) cos(x)

Cosine

cos(2x) = cos^2(x) -sin^2(x)  cos(2x) = 1 -2sin^2(x)  cos(2x) = 2cos^2(x) -1

Tangent

tan(2x) = \frac{2tan(x)}{1-tan^2(x)}

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