证明tan^2x=2*tan^2y+1,求证sin^2y=2sin^2x-1
问题描述：
证明tan^2x=2*tan^2y+1,求证sin^2y=2sin^2x-1
答
tan^2x=2*tan^2y+1;
sin^2x=tan^2x/(1+tan^2x);
sin^2y=tan^2y/(1+tan^2y);
sin^2y-2sin^2x+1=tan^2y/(1+tan^2y)-2*tan^2x/(1+tan^2x)+1
=tan^2y/(1+tan^2y)-2*(2*tan^2y+1)/(1+2*tan^2y+1)+1
=(tan^2y-2tan^2y-1)/(1+tan^2y)+1=0;
所以sin^2y=2sin^2x-1.