cos4^π/8-sin4^π/8等于

题目详情

cos4^π/8-sin4^π/8等于

▼优质解答

答案和解析

cos^4(π/8)-sin^4(π/8)
=[cos^2(π/8)+sin^2(π/8)][cos^2(π/8)-sin^2(π/8)] (平方差公式)
=1*[cos^2(π/8)-sin^2(π/8)]
=cos(π/8+π/8) (cos2倍角公式)
=cosπ/4=根号2/2

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