求值cos(2arctan根号6+pai/3)
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求值cos(2arctan根号6+pai/3)
cos(2arctan根号6+π/3)
=cos(2arctan根号6)cos(π/3)-sin(2arctan根号6)sin(π/3)
={2cos^2(arctan根号6)-1}*1/2-2sin(arctan根号6)cos(arctan根号6)*1/2*根号3
=cos^2(arctan根号6)-1/2-sin(arctan根号6)cos(arctan根号6)*根号3
又因为 cos(arctan根号6)= 1/根号7 sin(arctan根号6)=根号6/根号7
=1/7-1/2-3/7*根号2
=-5/14-3/7*根号2
=cos(2arctan根号6)cos(π/3)-sin(2arctan根号6)sin(π/3)
={2cos^2(arctan根号6)-1}*1/2-2sin(arctan根号6)cos(arctan根号6)*1/2*根号3
=cos^2(arctan根号6)-1/2-sin(arctan根号6)cos(arctan根号6)*根号3
又因为 cos(arctan根号6)= 1/根号7 sin(arctan根号6)=根号6/根号7
=1/7-1/2-3/7*根号2
=-5/14-3/7*根号2
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