# 9.2E: Sum and Difference Identities (Exercises)

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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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