根号下sin²150°+cos²35°+2sin210°cos²145° 等于?
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根号下sin²150°+cos²35°+2sin210°cos²145° 等于?
根号下sin²150°+cos²35°+2sin210°cos²145° 等于?
根号下sin²150°+cos²35°+2sin210°cos²145° 等于?
sin²150°=sin²30°=1/4
cos²35°+2sin210°cos²145°=cos²35°+2sin210°cos²35°=cos²35°(1-2sin30°)=0
所以根号下那个式子等于1/2
√(sin²150°+cos²35°+2sin210°cos145°)
=√[sin²30°+cos²35°+2sin(180°+30°)cos(180°-145°)]
√[sin²30°+cos²35°+2sin30°cos35°]
=√[sin30°+cos35°]²
=sin30°+cos35°