Answer:
1
Step-by-step explanation:
Using the trig. identity
sin²x + cos²x = 1
Given
[tex]\frac{sin^4x-cos^4x}{sin^2x-cos^2x}[/tex]
[tex]sin^{4}[/tex]x - [tex]cos^{4}[/tex]x ← is a difference of squares and factors as
(sin²x - cos²x)(sin²x + cos²x), then fraction becomes
= [tex]\frac{(sin^2x-cos^2x)(sin^2x+cos^2x)}{sin^2x-cos^2x}[/tex] ← cancel (sin²x - cos²x) on numerator/ denominator
= sin²x + cos²x
= 1
