sin²5 + sin²10 + sin²15 + ••• + sin²85° + sin²(90°) =?
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Answered by
1
Answer:
sin θ = cos (90° – θ);
sin (90° – θ) = cos θ
∴ sin 85° = sin (90° – 5°) = cos 5°
∴ (sin² 5° + sin² 85°) + (sin² 10° + sin² 80°) + ... to 8 terms + sin² 45° + sin² 90°
8 \times 1 + \frac{1}{2} + 1 = 9 \frac{1}{2}8×1+
2
1
+1=9
2
1
Answered by
3
Answer:
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Step-by-step explanation:
sin θ = cos (90° – θ);
sin (90° – θ) = cos θ
∴ sin 85° = sin (90° – 5°) = cos 5°
∴ (sin² 5° + sin² 85°) + (sin² 10° + sin² 80°) + to 8 terms + sin² 45° + sin² 90°
= 8 × 1 + 1/2 +1 =9 1/2
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