sin²5° + sin²10° + sin²15° + .... + sin²85°

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sin²5° + sin²10° + sin²15° + .... + sin²85° + sin²90° is equal to

1. 7 1
  2
2. 8 1
  2
3. 9
4. 9 1
  2

Correct Option: D

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	+ 1 = 9	1
		2		2