(3/sin^2140°-1/cos^2140°)*1/2sin10°的值

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(3/sin^2140°-1/cos^2140°)*1/2sin10°的值

(3/sin^2140°-1/cos^2140°)*1/2sin10°的值
(3/sin^2140°-1/cos^2140°)*1/2sin10°的值

(3/sin^2140°-1/cos^2140°)*1/2sin10°的值
(3/sin²140-1/cos²140)/(2sin10)
=[(3cos²140-sin²140)/(sin²140cos²140)]/(2sin10)
=4[((√3cos140+sin140)(√3cos140-sin140)/sin²280]/(2sin10)
=4[((√3cos40-sin40)(√3cos40+sin40)/sin²80]/(2sin10)
=[16sin(60+40)sin(60-40)/cos²10]/(2sin10)
=(16sin100sin20)/(2sin10cos²10)
=[(16cos10*2cos10sin10)/(2sin10cos²10)
=(32sin10cos²10)/(2sin10cos²10)
=16