化简:sin^2(42°+α)-2tan(25°+α)tan(65°-α)+sin^2(48°-α)-cot^2(990°-α)
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化简:sin^2(42°+α)-2tan(25°+α)tan(65°-α)+sin^2(48°-α)-cot^2(990°-α)
化简:sin^2(42°+α)-2tan(25°+α)tan(65°-α)+sin^2(48°-α)-cot^2(990°-α)
化简:sin^2(42°+α)-2tan(25°+α)tan(65°-α)+sin^2(48°-α)-cot^2(990°-α)
-(tanα的平方) -1.你要发现42°+α与48°-α互余,25°+α与65°-α互余.正切余切的周期是180°,故最后一个可化为90°-α,可得到最后一个为tanα的平方
原式=
=sin^2(42°+α)-2tan(25°+α)*[1/tan(25°+α)+]cos^2(42°+α)-cot^2(990°-α)
=1-2-cot^2(-90º-a)
=-1-tan²a
=-[1+sin²a/cos²a]
= - 1/cos²a
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化简:sin^2(42°+α)-2tan(25°+α)tan(65°-α)+sin^2(48°-α)-cot^2(990°-α)
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