证明:left =[(sinx+tanx)/(cscx+cotx)]2
=[(sinx+tanx)/(1/sinx+1/tanx)]^2
={(sinx+tanx)/[(sinx+tanx)/(sinx*tanx)]}^2
= sin^x*tan^x
right =[(sinx)2+(tanx)2]/[(cscx)2+(cotx)2]
=[(sinx)^2+(tanx)^2]/[1/(sinx)^2+1/(tanx)^2]
=[(sinx)^+(tanx)^/[(sin^x+tan^x)/(sin^x*tan^x)]
=sin^x*tan^x
左=右，领证。
用三角函数线证明:设P(a，b)，|OP|=c
- gt；sinX=a/c，tanX=a/b，cscX=c/a，cotX=b/a
左边= [(sinx+tanx)/(cscx+cotx)]
=[(a/c+a/b)/(c/a+b/a)]
={[a(b+c)/bc]/[(b+c)/a]}
={[a(b+c)/bc]/[(b+c)/a]}
=[a /(bc)]
Right = [sinx+tanx]/[cscx+cotx]
=(a /c +a /b )/(c /a +b /a)
=[a (b +c )/(b c )]/[(b +c )/a ]
=[a^4/(b c )]
=[a /(bc)]
左=右，领证。
