若cos(x-30°)=5/13,-60°小于x小于30°,则cosx=_数学解答

若cos(x-30°)=5/13,-60°小于x小于30°,则cosx=

人气：282 ℃　时间：2020-06-03 20:50:52

解答

-60°-90°sin(x-30°)<0
sin(x-30°)
=-√[1-cos²(x-30°)]
=-√[1-(5/13)²]=-12/13
cosx
=cos[(x-30°)+30°]
=cos(x-30°)cos30°-sin(x-30°)sin30°
=5/13×√3/2-(-12/13)×1/2
=(5√3+12)/26