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61. Table of Useful Formulæ. -The following is a list of important formulæ proved in this chapter, and summed for the convenience of the student:

up

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7. 2 cos x cos y

= cos x cos y + sin x siny.

= sin (x + y) + sin (x − y)

=

sin (x + y) sin (x − y).

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= cos (x + y) + cos (x − y).

8. 2 sinx siny = cos(x − y) — cos (x + y).

9. sinx + sin y = 2sin(x + y) cos † (x − y).

10. sinx siny 2 cos(x+y) sin(x − y).

=

11. cosx+cos y = 2 cos(x+y) cos(xy).

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19. sin (x+y) sin (xy)= sin2x-sin'y cos2y - cos2x.

20. cos (x+y) cos (xy)= cos2x-sin'y

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B

and cos ẞ=2, find a value for sin (« + ß),

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13. Simplify 2 cos 20 cos 0-2 sin 40 sin 0.

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21. cos (60° + A) + cos (60° — A) = cos A.

22. cos (45°+ A) + cos (45° - A) = √2cos A.

23. sin (45°+ A) sin (45°-A) = √2sin A.

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