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    Problems on trigonometric identities and equations

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    Prove this identity:

    7. sin(x+y)/sin(x-y) = coty +cotx / coty - cot x

    8. simplify:
    2 sinxcos³x - 2 sin³xcosx

    9. If cosx=-1/4 and pie/2<x<pie, the cos (pie/6 - x) = ?

    10. Prove this identity:
    cos 8x = cos²4x - sin²4x.

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    Solution Preview

    Please see the attached file.

    7. Prove: sin(x+y)/sin(x-y) = coty +cotx / coty - cot x
    We start from right hand side:
    We have

    . Hence proved.

    8. Simplify: 2 sinxcos³x - 2 ...

    Solution Summary

    Methods to simplify trigonometric expressions using simple and fundamental trigonometric identities are discussed.

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