和角公式与差角公式的应用
求[2sin50°+sin10°(1+√3*tan10°)]*√(2sin^80°)的值
解:[2sin50°+sin10°(1+√3*tan10°)]*√(2sin^80°)
=[2sin50°+sin10°(1+√3sin10°/cos10°)]*√(2sin^80°)
=[2sin50°+sin10°(cos10°+√3sin10°)/(cos10°)]*√(2sin^80°)
=[2sin50°+2sin10°(1/2cos10°+√3/2sin10°)/(cos10°)]*√(2sin^80°)
=[2sin50°+2sin10°(sin30°cos10°+cos30°sin10...全部
求[2sin50°+sin10°(1+√3*tan10°)]*√(2sin^80°)的值
解:[2sin50°+sin10°(1+√3*tan10°)]*√(2sin^80°)
=[2sin50°+sin10°(1+√3sin10°/cos10°)]*√(2sin^80°)
=[2sin50°+sin10°(cos10°+√3sin10°)/(cos10°)]*√(2sin^80°)
=[2sin50°+2sin10°(1/2cos10°+√3/2sin10°)/(cos10°)]*√(2sin^80°)
=[2sin50°+2sin10°(sin30°cos10°+cos30°sin10°)/(cos10°)]*√(2sin^80°)
=[2sin50°+(2sin10°sin40°)/(cos10°)]*√(2sin^80°)
=[(2sin50°cos10°+2sin10°sin40°)/(cos10°]*√(2sin^80°)
=2[(sin50°cos10°+sin10°cos50°)/(cos10°)]*√(2sin^80°)
=2[(sin50°cos10°+sin10°cos50°)/(cos10°)]*√(2sin^80°)
=2[(sin60°/(cos10°)]*√(2sin^80°)
=2[(√3/2)/(cos10°)]*√(2sin^80°)
=[√3/(cos10°)]*√(2sin^80°)
=[√3/(cos10°)]*√2*sin80°
=√3*√2*sin80°/(cos10°)
=√6*cos10°/(cos10°)
=√6
。
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