cos^2(5π/12)+cos^2(π/12)+cos(5π/12)*cos(π/12)的值等于______________.
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解法如下:因为,cos(5π/12)=cos(π/2-π/12)=sin(π/12)所以,cos(5π/12)*cos(π/12)=sin(π/12)*cos(π/12)=sin(π/6)/2=1/4同理,cos^2(5π/12)+cos^2(π/12)=sin^2(π/12)+cos^2(π/12)=1所以,原式=5/4
cos^2(5π/12)+cos^2(π/12)+cos(5π/12)*cos(π/12)的值等于______________.
解法如下:因为,cos(5π/12)=cos(π/2-π/12)=sin(π/12)所以,cos(5π/12)*cos(π/12)=sin(π/12)*cos(π/12)=sin(π/6)/2=1/4同理,cos^2(5π/12)+cos^2(π/12)=sin^2(π/12)+cos^2(π/12)=1所以,原式=5/4