已知sina+cosa=m 求sina*cosa 和 sin^4a+cos^4a的值
问题描述:
已知sina+cosa=m 求sina*cosa 和 sin^4a+cos^4a的值
答
sina+cosa=m(sina+cosa)^2=m^21+2sinacosa=m^22sinacosa=m^2-1sinacosa=(m^2-1)/2sin^2acos^2a=(m^2-1)^2/4sin^4a+cos^4a=(sin^2a+cos^2a)^2-2sin^2acos^2a=1-2sin^2acos^2a=1-2*(m^2-1)^2/4=1-(m^2-1)^2/2=1-(m^4-2...