为啥sina+cosa=√2sin(a+π/4)

为啥sina+cosa=√2sin(a+π/4) 已知(sina+cosa)/(sina-cosa)=3 则2sin'a+(sina-cosa)'=? √2(cos^2a-sin^2a)/(sina-cosa)=-2√2/2,则cosa+sina=? 若θ,a为锐角且tanθ=(sina-cosa)/(sina+cosa),求证：sina-cosa=√2sinθ. sina=2cosa,求(1)3sina+2cosa(2)sin²a+sina×cosa+3 cos^2a-sin^2a=(cosa+sina)(cosa-sina)吗?求解 三角函数恒等式求证：cosa + sina / cosa - sina + cosa - sina / cosa + sina = cos＾2a - sin＾2a / 2 sina+cosa/sina-cosa=2 求sin^2a-2sinacosa+1 求证：cosa(cosa-cosb)+sina(sina-sinb)=2sin^2a-b/2 已知tana=-3,求sina+2cosa/cosa-3sina和sin^2a-sinacosa sinA=3sin(2π/3-A) SINA=?sinA=3sin(2π/3-A) SINA=?答案是-3√3cosA 当a为钝角时,sina/√1-cos^2 a - cosa/√1-sin^2 a的值是解法原式=sina/|sina|-cosa/|cosa| =sina/sina-cosa/(-cosa) =2我想问的是为什么在cosa/|cosa|中,分子|cosa|要变负号,而分母cosa不用? 已知(sina+cosa)/(sina-cosa)=2,则：(3sina+cosa)/(2sina+3cosa)=?sin^2a-2sinacosa+1=? 已知sina+cosa/sina-cosa=2,计算下列各式的值（1）3sina+cosa/2sina+3cosa(2)sin^a-2sinacosa+1. 已知tana=3,求下列各式的值 1.sina+cosa/sina-cosa 2.sina.cosa 3.sin^2 a+sina.cosa cosa/(sina+sin3a)=cosa/(2sin(2a)cosa)怎么来的啊 已知sin a+cos a=1/2 sina*cosa=?cos a/sina+sina/cosa=? tan a=2 ,2sina cosa=?(sin a )^2-sina cosa -2(cosa)^2=?