三角比证明

证明：左=[(sinX+tanX)/(cscX+cotX)]^2

=[(sinX+tanX)/(1/sinX+1/tanX)]^2 文章源自玩技e族-https://www.playezu.com/91283.html

={(sinX+tanX)/[(sinx+tanx)/(sinX*tanX)]}^2 文章源自玩技e族-https://www.playezu.com/91283.html

= sin^x*tan^x 文章源自玩技e族-https://www.playezu.com/91283.html

右=[(sinX)^2+(tanX)^2]/[(cscX)^2+(cotX)^2] 文章源自玩技e族-https://www.playezu.com/91283.html

=[(sinX)^2+(tanX)^2]/[1/(sinX)^2+1/(tanX)^2] 文章源自玩技e族-https://www.playezu.com/91283.html

=[(sinX)^+(tanX)^/[(sin^x+tan^x)/(sin^X*tan^X)] 文章源自玩技e族-https://www.playezu.com/91283.html

=sin^x*tan^x 文章源自玩技e族-https://www.playezu.com/91283.html

左边=右边，得证文章源自玩技e族-https://www.playezu.com/91283.html

  用三角函数线证明：设P(a,b),|OP|=c 文章源自玩技e族-https://www.playezu.com/91283.html

--->sinX=a/c,tanX=a/b,cscX=c/a,cotX=b/a 文章源自玩技e族-https://www.playezu.com/91283.html

左边=[(sinX+tanX)/(cscX+cotX)]²

=[(a/c+a/b)/(c/a+b/a)]²

={[a(b+c)/bc]/[(b+c)/a]}²

={[a(b+c)/bc]/[(b+c)/a]}²

=[a²/(bc)]²

右边=[sin²X+tan²X]/[csc²X+cot²X]

=(a²/c²+a²/b²)/(c²/a²+b²/a²)

=[a²(b²+c²)/(b²c²)]/[(b²+c²)/a²]

=[a^4/(b²c²)]

=[a²/(bc)]²

左边=右边，得证。