Answer:
sin⁴x - sin²x = cos⁴x - cos²x
Solve the right hand side of the equation
That's
sin⁴x - sin²x
From trigonometric identities
sin²x = 1 - cos²x
So we have
sin⁴x - ( 1 - cos²x)
sin⁴x - 1 + cos²x
sin⁴x = ( sin²x)(sin²x)
That is
( sin²x)(sin²x)
So we have
( 1 - cos²x)(1 - cos²x) - 1 + cos²x
Expand
1 - cos²x - cos²x + cos⁴x - 1 + cos²x
1 - 2cos²x + cos⁴x - 1 + cos²x
Group like terms
That's
cos⁴x - 2cos²x + cos²x + 1 - 1
Simplify
We have the final answer as
cos⁴x - cos²x
So we have
cos⁴x - cos²x = cos⁴x - cos²x
Since the right hand side is equal to the left hand side the identity is true
Hope this helps you