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2 cos a sin b = sin (a + b) - sin (a - b)
••
2 cos (x + 45°) sin (x - 45°)
= sin (x + 45° + x - 45°) - sin (x + 45° - x + 45°)
= sin 2x - sin 90°
= sin 2x - 1
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ㅜЯไGΘИΘMξㅜЯไ
2 cos a sin b = sin (a + b) - sin (a - b)
••
2 cos (x + 45°) sin (x - 45°)
= sin (x + 45° + x - 45°) - sin (x + 45° - x + 45°)
= sin 2x - sin 90°
= sin 2x - 1
=> sin ((x+45)+(x-45)) - sin ((x+45)-(x-45))
=> sin (x+45+x-45) - sin (x+45-x+45)
=> sin (2x) - sin (90)
=> sin 2x - 1