计算sin²10°+sin²50°+sin10°s - 知识问答

计算sin²10°+sin²50°+sin10°sin50°的值详细答案

2个回答

【注：单位是度.】
可设原式=y.
2y=2sin²10+2sin²50+2sin10sin50
=(1-cos20)+(1-cos100)+2sin10sin50
=2-(cos100+cos20)+2sin10sin50
=2-cos40+2sin10cos40
=2-sin50+sin50-sin30
=2-(1/2)
=3/2
∴原式=3/4

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