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
Explanation:
Use:
a^2-b^2 = (a-b)(a+b)a2−b2=(a−b)(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))(1−1)
= 0=0