sin2 5 deg sin2 10 deg sin2 15 deg sin2 85 deg sin2 90 deg is equal to ........

Quantitative Aptitude ( CCS) Trignometry

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sin² 5° + sin² 10° + sin² 15° + ... + sin² 85° + sin² 90° is equal to

7 1/2

8 1/2

9 1/2

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Explanation:

sin² 5° + sin² 10° + sin² 15° + ..... + sin² 85° + sin² 90°
= (sin² 5° + sin² 85°) + (sin² 10° + sin² 80°) + ..... to 8 terms + sin² 45° + sin² 90°
= (sin² 5° + cos² 5°) + (sin² 10° + cos² 10°) + .... to 8 terms + sin² 45° + sin² 90°
[? sin (90° – Θ) = cos Θ]
= 1 + 1 + ... to 8 terms + (1/√2)²+ (1)²
= 8 + 1/2 + 1
= 9 1/2