求值：sin(π/12)+cos(π/12)

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求值：sin(π/12)+cos(π/12)求值：sin(π/12)+cos(π/12)求值：sin(π/12)+cos(π/12)[sin(π/12)+cos(π/12)]^2=[sin(π/12)

求值：sin(π/12)+cos(π/12)
求值：sin(π/12)+cos(π/12)

求值：sin(π/12)+cos(π/12)
[sin(π/12)+cos(π/12)]^2
=[sin(π/12)]^2+2sin(π/12)*cos(π/12)+[cos(π/12)]^2
=1+22sin(π/12)*cos(π/12)
=1+sin(π/6)
=1+1/2=3/2
因为sin(π/12)+cos(π/12)>0
所以sin(π/12)+cos(π/12)=√(3/2)=√6/2