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

(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