How do you simplify sin^4(x)-cos^4(x)-sin^2(x)+cos^2(x)sin4(x)cos4(x)sin2(x)+cos2(x) ?

1 Answer
Oct 21, 2016

sin^4(x) - cos^4(x)-sin^(2)x+cos^2(x) = 0sin4(x)cos4(x)sin2x+cos2(x)=0

Explanation:

Use:

a^2-b^2 = (a-b)(a+b)a2b2=(ab)(a+b)

sin^2(x) + cos^2(x) = 1sin2(x)+cos2(x)=1

as follows:

sin^4(x) - cos^4(x)-sin^(2)(x)+cos^2(x)sin4(x)cos4(x)sin2(x)+cos2(x)

= (sin^4(x) - cos^4(x))-(sin^(2)(x)-cos^2(x))=(sin4(x)cos4(x))(sin2(x)cos2(x))

= (sin^2(x) - cos^2(x))(sin^2(x)+cos^2(x))-(sin^(2)(x)-cos^2(x))=(sin2(x)cos2(x))(sin2(x)+cos2(x))(sin2(x)cos2(x))

= (sin^2(x) - cos^2(x))(sin^2(x)+cos^2(x)-1)=(sin2(x)cos2(x))(sin2(x)+cos2(x)1)

= (sin^2(x) - cos^2(x))(1-1)=(sin2(x)cos2(x))(11)

= 0=0