How do you simplify #sin^4(x)-cos^4(x)-sin^2(x)+cos^2(x)# ?
1 Answer
Oct 21, 2016
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#
