（1）sin^2x/(sec^2x-1)+cos^2x/(csc^2x-1)
=sin^2x/tan^2x+cos^2x/cot^2x
=cos^2x+sin^2x
=1
（2）题目出错了，不等于1的
（3）①cos(A+B)=cos(π-C)=-cosC
②sin(2A+2B)=sin[2(A+B)]=sin[2(π-C)]=sin(2π-2C)=-sin2C
③cos(2A+2B)=cos[2(A+B)]=cos[2(π-C)]=cos(2π-2C)=cos2C
（4）[1+(1-cosθ)/(1+cosθ)][1+(1+cosθ)/(1-cosθ)]
=(1+cosθ+1-cosθ)/(1+cosθ)*(1-cosθ+1+cosθ)/(1-cosθ)
=4/(1-cos^2θ)
=4/sin^2θ
=4csc^2θ
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