Answer:
tan²Θ
Step-by-step explanation:
simplify the expression using the identities
secΘ = [tex]\frac{1}{cos0}[/tex]
tan²Θ = sec²Θ - 1
then
[tex]\frac{cos0-cos^30}{cos^30}[/tex] ( divide each term on the numerator by cos³Θ
= [tex]\frac{cos0}{cos^30}[/tex] - [tex]\frac{cos^30}{cos^30}[/tex]
= [tex]\frac{1}{cos^20}[/tex] - 1
= sec²Θ - 1
= tan²Θ
Answer:
[tex]\tan^2(\theta)[/tex]
Step-by-step explanation:
Assuming this is
[tex]\dfrac{\cos(\theta)-cos^3(\theta)}{cos^3(\theta)}[/tex]
Trig identities used:
[tex]\sin^2(\theta)+\cos^2(\theta)=1 \implies 1-\cos^2(\theta)=\sin^2(\theta)[/tex]
[tex]\dfrac{\cos(\theta)-cos^3(\theta)}{cos^3(\theta)}[/tex]
[tex]=\dfrac{\cos(\theta)(1-cos^2(\theta))}{cos^3(\theta)}[/tex]
[tex]=\dfrac{1-cos^2(\theta)}{cos^2(\theta)}[/tex]
[tex]=\dfrac{sin^2(\theta)}{cos^2(\theta)}[/tex]
[tex]=\tan^2(\theta)[/tex]
