求sin^10°+cos^40°+sin10°cos40°

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求sin^10°+cos^40°+sin10°cos40°
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求sin^10°+cos^40°+sin10°cos40°
求sin^10°+cos^40°+sin10°cos40°

求sin^10°+cos^40°+sin10°cos40°
运用余弦定理可得
因为c^2=a^2+b^2-2abcosC
运用正弦定理可得
(2rsinC)^2=(2rsinA)^2+(2rsinB)^2-2(rsinA)(rsinB)cosC
所以(sinC)^2=(sinA)^2+(sinB)^2-2sinAsinBcosC
原式=sin^2(10°)+sin^2(50°)+sin10°sin50°
=sin^2(10°)+sin^2(50°)-2sin10°sin50°cos120°
=sin^2(120°)
=3/4