Question

Simplify (sin^4(x) - cos^4(x)) / (sin^2(x) - cos^2(x))

Answer 1

1

Explanation:

Using the trig. identity

sin²x + cos²x = 1

Given

`(sin^4x-cos^4x)/(sin^2x-cos^2x)`

`sin^(4)`x -
`cos^(4)`x ← is a difference of squares and factors as

(sin²x - cos²x)(sin²x + cos²x), then fraction becomes

=
`((sin^2x-cos^2x)(sin^2x+cos^2x))/(sin^2x-cos^2x)` ← cancel (sin²x - cos²x) on numerator/ denominator

= sin²x + cos²x

= 1