cos75°*cos15°-sin225°*sin15°的值为？
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cos75°*cos15°-sin225°*sin15°
= cos75°*cos15°- sin(180°+ 45°)*sin15°
= cos75°*cos15°+ sin45°*sin15°
= (√6-√2)/4 × (√6+√2)/4 + √2/2 × (√6-√2)/4
= (6-2)/16 + √2/2 × (√6-√2)/4
= 1/4 + √2/2 × (√6-√2)/4
= 1/4 + (√12-√4)/8
= 1/4 + (2√3-2)/8
= 1/4 + (√3-1)/4
= √3/4
= cos75°*cos15°- sin(180°+ 45°)*sin15°
= cos75°*cos15°+ sin45°*sin15°
= (√6-√2)/4 × (√6+√2)/4 + √2/2 × (√6-√2)/4
= (6-2)/16 + √2/2 × (√6-√2)/4
= 1/4 + √2/2 × (√6-√2)/4
= 1/4 + (√12-√4)/8
= 1/4 + (2√3-2)/8
= 1/4 + (√3-1)/4
= √3/4
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