Answered

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Solve the trigonometric function
cos∅ - cos^3 ∅ / cos^3 ∅

Sagot :

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

semsee45

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]

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