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sin² 5° + sin² 6° + ... + sin² 84° + sin² 85° = ?
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39 1 2 -
40 1 2 - 40
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39 1 √3
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Correct Option: B
Let the number of terms be n, then
By t 2 = a + (n – 1)d
85 = 5 + (n –1)
⇒ n – 1 = 85 – 5 = 80
⇒ n = 81
∴ sin²5° + sin²6°+ ... + sin²45° + ... + sin² 84° + sin² 85°
= (sin²5° + sin²85°) + (sin²6° + ... + sin² 84°) + ..... + to (40 terms) + sin²45°
= (sin²5° + cos25°) + (sin²6° + ... + cos² 6°) + ..... + to 40 terms + sin²45°
