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  • Perplex
    IB Math AAHL
    /
    Trig equations & identities
    /

    Further trigonometric identities

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    Exercises

    Key Skills

    Further trigonometric identities

    Further trigonometric identities

    Compound angle identities ​sin(A+B)​ and ​cos(A+B), double angle identity for ​tan2θ, and pythagorean identity for reciprocal trig functions.

    Want a deeper conceptual understanding? Try our interactive lesson! (Plus Only)

    Exercises

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    Practice exam-style further trigonometric identities problems

    Key Skills

    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​📖
    ​