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Further trigonometric identities
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Further trigonometric identities, including the compound angle formulas for \(\sin(A\pm B)\), \(\cos(A\pm B)\) and \(\tan(A\pm B)\), the double angle identity \(\tan 2\theta=\frac{2\tan\theta}{1-\tan^2\theta}\), and the identities \(1+\tan^2\theta=\sec^2\theta\) and \(1+\cot^2\theta=\cosec^2\theta\).
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Sine and Cosine Compound Angle Identities
AHL 3.10
sin(A±B) cos(A±B)=sinAcosB±cosAsinB📖 =cosAcosB∓sinAsinB📖
1+tan²θ=sec²θ
AHL 3.9
If we take the identity sin2θ+cos2θ=1 and divide through by cos2θ we find
1+tan2θ=sec2θ📖
1+cot²θ=cosec²θ
AHL 3.9
If we take the identity sin2θ+cos2θ=1 and divide through by sin2θ we find
1+cot2θ=cosec2θ📖
Tan Double Angle Identity
AHL 3.10
The double angle identity for tan states that
tan2θ=1−tan2θ2tanθ📖
Tan Compound Angle Identity
AHL 3.10
The compound angle identity for tan states that
tan(A±B)=1∓tanAtanBtanA±tanB📖
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