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Q.

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

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a

2

b

1

c

0

d

3

answer is D.

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Detailed Solution

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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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