化简根号1-sin200°
√( 1 - sin200° )
= √[ (sin100°)^2 + (cos100°)^2 - 2sin100°cos100° ]
= √[ ( sin100° + cos100°)^2 ]
【 ∵ sin100° + cos100° > 0 】
= sin100° + cos100°
= √2sin(100° + 45° )
= √2sin(180° - 35° )
= √2sin35° 。
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√( 1 - sin200° )
= √[ (sin100°)^2 + (cos100°)^2 - 2sin100°cos100° ]
= √[ ( sin100° + cos100°)^2 ]
【 ∵ sin100° + cos100° > 0 】
= sin100° + cos100°
= √2sin(100° + 45° )
= √2sin(180° - 35° )
= √2sin35° 。