9.2E: Sum and Difference Identities (Exercises)

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Dec 26, 2024
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- 9.2: Sum and Difference Identities
- 9.3: Double-Angle, Half-Angle, and Reduction Formulas

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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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