Find the value of sin² 15° + sin² 25° + sin² 33° + sin² 57° + sin² 65° + sin² 75°.

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answer is D.

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Detailed Solution

Given, sin² 15° + sin² 25° + sin² 33° + sin² 57° + sin² 65° + sin² 75°

= sin² (90° - 75°) + sin² (90° - 65°) + sin² (90° - 57°) + sin² 57° + sin² 65° + sin² 75°

= cos² 75° + cos² 65° + cos² 57° + sin² 57° + sin² 65° + sin² 75°

= (sin² 57° + cos² 75°) + (sin² 65° + cos² 65°) + (sin² 57° + cos² 57°)

= 1 + 1 + 1..... [Since, sin² θ + cos² θ = 1]

= 3.

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