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100 POINTS AND BRAINLIEST!! PRE CALC!

The trigonometric relation cos (π/3 + x) + cos (π/3 - x) is equivalent to:

a. cos 2x
b. cos x
c. sin x
d. 1/2 cos x

Please explain your answer :)

Respuesta :

RedGeek2531

Answer:

b

Step-by-step explanation:

use cos(r + s ) = cosrcoss - sinrsins to expand.

cos pi/3 cosx - sin pi/3 sinx + cos pi/3 cosx + sin pi/3 sinx

the two in bold cancel out.

cospi/3 cosx + cospi/3 cosx

pi = 180° in trigonometry.

cos 180/3 cosx + cos 180/3 cosx

1/2 cosx + 1/2 cosx

= cos x
  • cos(A+B)+cos(A-B)=2cosAcosB

Hence

  • cos(π/3+x)+cos(π/3-x)
  • 2cosπ/3(cosx)
  • 2(1/2)(cosx)
  • cosx

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