怎么证明tan^2A+cot^2A不等于1
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怎么证明tan^2A+cot^2A不等于1
tan^2A+cot^2A
=sin^2A/cos^2A+cos^2A/sin^2A
=sin^4A+cos42A/sin^2A*cos^2A
=sin^4A+cos42A/(1/4*sin^22A)
=4*sin^4A+4*cos42A/sin^22A
=[4*sin^4A-4*sin^2A+1+4*cos^4A-4*cos^2A+1+4*sin^2A+4cos^2A-1-1]/sin^22A
=[(1-2*sin^2A)^2+(2*cos^2A-1)^2+4*(sin^2A+cos^2A)-2]/sin^22A
=[cos^22A+cos^22A+4-2]/sin^22A
=[2cos^22A+2]/sin^22A
因为:2cos^22A+2>=2,sin^22A
=sin^2A/cos^2A+cos^2A/sin^2A
=sin^4A+cos42A/sin^2A*cos^2A
=sin^4A+cos42A/(1/4*sin^22A)
=4*sin^4A+4*cos42A/sin^22A
=[4*sin^4A-4*sin^2A+1+4*cos^4A-4*cos^2A+1+4*sin^2A+4cos^2A-1-1]/sin^22A
=[(1-2*sin^2A)^2+(2*cos^2A-1)^2+4*(sin^2A+cos^2A)-2]/sin^22A
=[cos^22A+cos^22A+4-2]/sin^22A
=[2cos^22A+2]/sin^22A
因为:2cos^22A+2>=2,sin^22A
怎么证明tan^2A+cot^2A不等于1
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