已知 tan平方x=2tan平方y+1求证 sin平方y=2sin平方x-1
热心网友
解:
热心网友
(tanx)^2=2(tany)^2+1---1+(tanx)^2=2[(tany)^2+1)]---(secx)^2=2(secy)62---(cosx)^2=(cosy)^2/2---1-(cosx)^2=1-(cosy)^2/2---(sinx)^2=[2-(cosy)^2)]/2---2(sinx)^2=1+[1-(cosy)^2]---(siny)^2=2(sinx)^2-1
热心网友
已知： tgx^2=2tgy^2+1 求证 siny^2=2sinx^2-1证明：tgx^2=2tgy^2+1 展开sinx^2/cosx^2=2siny^2/cosy^2 +1sinx^2*cosy^2=2siny^2*cosx^2+cosy^2*cosx^2即：sinx^2*(1-siny^2)=2siny^2*(1-sinx^2)+(1-sinx^2)(1-siny^2)即：sinx^2-sinx^2*siny^2=2siny^2-2siny^2sinx^2+1-sinx^2-siny^2+sinx^2*siny^2两边相减，整理即得：siny^2+1-2sinx^2＝0∴ siny^2=2sinx^2-1 (得证)