The value of expression cos245° + cos2135° + cos2225° + cos2315° is:

cos245° + cos2135° + cos2225° + cos2315° = (cos245° + cos2315°) + (cos2135° + cos2225°) [Here cos2α + cos2β = 1, where α + β = 360°] = 1 + 1 = 2

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This question belongs to Arithmetic Ability Trigonometry

Trigonometry

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The value of expression cos²45° + cos²135° + cos²225° + cos²315° is:

A) 2 B) $$\frac{1}{2}$$ C) $$\frac{3}{2}$$ D) 1

Answer & Solution

Correct Answer: Option A

cos²45° + cos²135° + cos²225° + cos²315°
= (cos²45° + cos²315°) + (cos²135° + cos²225°) [Here cos²α + cos²β = 1, where α + β = 360°]
= 1 + 1
= 2

Question posted by Examveda

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