Questions in trigonometry

Question # 1

Prove that cos(A + pi/3) + cos( A - pi/3) = cos(A).

Apply the sum of angle formula for cos.

cos(A + pi/3) = cos(A) cos(pi/3) - sin(A) sin(pi/3)
cos(A - pi/3) = cos(A) cos(pi/3) + sin(A) sin(pi/3)

Add the equations.

cos(A + pi/3) + cos(A - pi/3) = 2 cos(A) cos(pi/3).

cos(pi/3) = 1/2
cos(A + pi/3) + cos(A - pi/3) = 2 cos(A) (1/2) = cos(A)

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