数学题cos²75°+cos²15°+4cos²75°·cos²15°的值等于
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![数学题cos²75°+cos²15°+4cos²75°·cos²15°的值等于](/uploads/image/z/8853346-10-6.jpg?t=%E6%95%B0%E5%AD%A6%E9%A2%98cos%26%23178%3B75%C2%B0%EF%BC%8Bcos%26%23178%3B15%C2%B0%EF%BC%8B4cos%26%23178%3B75%C2%B0%C2%B7cos%26%23178%3B15%C2%B0%E7%9A%84%E5%80%BC%E7%AD%89%E4%BA%8E)
数学题cos²75°+cos²15°+4cos²75°·cos²15°的值等于
数学题cos²75°+cos²15°+4cos²75°·cos²15°的值等于
数学题cos²75°+cos²15°+4cos²75°·cos²15°的值等于
cos²75°+cos²15°+4cos²75°·cos²15°
=(cos²75°+sin²75°)+4sin²15°·cos²15°
=1+(sin30)^2
=1.25
cos²75°+cos²15°+4cos²75°·cos²15°
=cos²75°+sin²75°+4cos²75°·sin²75° (cos15=sin75)
=1+2sin(75*2) (2sin75cos75=sin150二倍角公式)
=1+2sin150
=1+2sin30
=2
cos²75°+cos²15°+4cos²75°·cos²15°=(cos75°+cos15°)²+2cos²75°·cos²15
因为cos15=(根号6+根号2)/4,cos75=(根号6-根号2)/4
代入即可得到答案为3/8+1/16=7/16