How do you simplify sin^4(x)-cos^4(x)-sin^2(x)+cos^2(x) ?

1 Answer
Oct 21, 2016

sin^4(x) - cos^4(x)-sin^(2)x+cos^2(x) = 0

Explanation:

Use:

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

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

as follows:

sin^4(x) - cos^4(x)-sin^(2)(x)+cos^2(x)

= (sin^4(x) - cos^4(x))-(sin^(2)(x)-cos^2(x))

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

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

= (sin^2(x) - cos^2(x))(1-1)

= 0