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9.2E: Sum and Difference Identities (Exercises)

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    56111
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    For the following exercises, find the exact value.

    11. \(\tan \left(\frac{7 \pi}{12}\right)\)

    12. \(\cos \left(\frac{25 \pi}{12}\right)\)

    13. \(\sin \left(70^{\circ}\right) \cos \left(25^{\circ}\right)-\cos \left(70^{\circ}\right) \sin \left(25^{\circ}\right)\)

    14. \(\cos \left(83^{\circ}\right) \cos \left(23^{\circ}\right)+\sin \left(83^{\circ}\right) \sin \left(23^{\circ}\right)\)

    For the following exercises, prove the identity.

    15. \(\cos (4 x)-\cos (3 x) \cos x=\sin ^{2} x-4 \cos ^{2} x \sin ^{2} x\)

    16. \(\cos (3 x)-\cos ^{3} x=-\cos x \sin ^{2} x-\sin x \sin (2 x)\)

    For the following exercise, simplify the expression.

    17. \(\frac{\tan \left(\frac{1}{2} x\right)+\tan \left(\frac{1}{8} x\right)}{1-\tan \left(\frac{1}{8} x\right) \tan \left(\frac{1}{2} x\right)}\)

    For the following exercises, find the exact value.

    18. \(\cos \left(\sin ^{-1}(0)-\cos ^{-1}\left(\frac{1}{2}\right)\right)\)

    19. \(\tan \left(\sin ^{-1}(0)+\sin ^{-1}\left(\frac{1}{2}\right)\right)\)


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