value of sin^2 15+ sin^2 645 equals to
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sin²15° + sin²645°
we know, sin(n × 360° - Ф) = -sinФ , use this here [ n is integers ]
Sin645° = sin(2 × 360 - 75°) = - sin75°
And we know, sin(90 - Ф) = cosФ
So, - sin75° = -sin(90-15°) = -cos15°
Hence, sin645° = -cos15°
Now, sin²15° + {-cos15°}²
= Sin²15 + cos²15°
= 1 [ ∵ sin²x + cos²x = 1 ]
Hence, answer should be 1
we know, sin(n × 360° - Ф) = -sinФ , use this here [ n is integers ]
Sin645° = sin(2 × 360 - 75°) = - sin75°
And we know, sin(90 - Ф) = cosФ
So, - sin75° = -sin(90-15°) = -cos15°
Hence, sin645° = -cos15°
Now, sin²15° + {-cos15°}²
= Sin²15 + cos²15°
= 1 [ ∵ sin²x + cos²x = 1 ]
Hence, answer should be 1
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