Question

sin²5 + sin²10 + sin²15 + ••• + sin²85° + sin²(90°) =?


hlo all​

Answer 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

Answer 2

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