√[sin^4(x)+4cos^2(x)] - √[cos^4(x)+4sin^2(x)]
√[sin^4(x)+4(1-sin^2(x))] - √[cos^4(x)+4(1-cos^2(x))]
√[sin^4(x)-4sin^2(x)+4] - √[cos^4(x)-4cos^2(x)+4]
√[(sin^2(x)-2)^2] - √[(cos^2(x)-2)^2]
The trap is here: √[x^2] does not equal x, it equals |x|. In this case sin^2(x)-2 and cos^2(x)-2 are always negative, so we get
-(sin^2(x)-2) - -(cos^2(x)-2)
cos^2(x) - sin^2(x) which is a double angle formula for
cos(2x) |
