设a为锐角,求证 根号3/2cosa+1/2sina=cos(π/6-a) cosa-sina=根号2cos(π/4+a)

来源:学生作业帮助网 编辑:六六作业网 时间:2024/05/14 05:16:33
设a为锐角,求证根号3/2cosa+1/2sina=cos(π/6-a)cosa-sina=根号2cos(π/4+a)设a为锐角,求证根号3/2cosa+1/2sina=cos(π/6-a)cosa-

设a为锐角,求证 根号3/2cosa+1/2sina=cos(π/6-a) cosa-sina=根号2cos(π/4+a)
设a为锐角,求证 根号3/2cosa+1/2sina=cos(π/6-a) cosa-sina=根号2cos(π/4+a)

设a为锐角,求证 根号3/2cosa+1/2sina=cos(π/6-a) cosa-sina=根号2cos(π/4+a)
根号3/2 cosa + 1/2sina
=cosπ/6 cosa + sinπ/6 sina
=cos(π/6-a)
cosa-sina
=根号2×根号2/2(cosa-sina)
=根号2×(cosπ/4 cosa - sinπ/4 sina)
=根号2cos(π/4+a)