Question

已知sina+cosa=二分之根号二,求1/sin^2a+1/cos^2a的值

已知sina+cosa=二分之根号二,求1/sin^2a+1/cos^2a的值

Answer 1

已知
sinA+COSA=二分之侍喊敏根号二 则sin^2A+cos^2A+2sinAcosa=1/2 sinAcosa=-1/4
1/sin^2a+1/cos^2a=sin^2A+cos^2A/sin^2Acos^2A=16
所以答案是16.小写a，我全渗袭部老枝用大写A、方便看而已

Answer 2

两边册蚂平知姿拦方得sin^2a+2sinacosa+cos^2a=1/2
1+2sinacosa=1/搭胡2
sinacosa=-1/4
1/sin^2a+1/cos^2a=(sin^2a+cos^2a)/sin^2a*cos^2a=1/1/16=16

Answer 3

1/(sina)^2+1/(cosa)^2=1/(sina)^2(cosa)^2=4/(sin2a)^2
由槐余sina+cosa=2^-0.5得
sin2a=-1/手明枝2
所以，毕敏原式=16