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1 vote
Cos 30° + cos60° + cos290° + 2 cos 30° cos 60° cos 90°

1 Answer

5 votes

Answer:

Using the trigonometric identity,

cos(A+B) = cosAcosB - sinAsinB

cos 30° + cos 60° + cos 290° + 2 cos 30° cos 60° cos 90°

= cos 30° + cos 60° + cos (360° - 70°) + 2 cos 30° cos 60° (0)

= cos 30° + cos 60° + cos 70°

= √3/2 + 1/2 + cos 70°

Using the identity,

cos(90° - A) = sinA

cos 70° = sin(90° - 70°) = sin20°

√3/2 + 1/2 + cos 70° = √3/2 + 1/2 + sin20°

Therefore, the final answer is √3/2 + 1/2 + sin20°.

answered
User Grapes
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