Question

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

Answer 1

tan²Θ

Explanation:

simplify the expression using the identities

secΘ =
`(1)/(cos0)`

tan²Θ = sec²Θ - 1

then

`(cos0-cos^30)/(cos^30)` ( divide each term on the numerator by cos³Θ

=
`(cos0)/(cos^30)` -
`(cos^30)/(cos^30)`

=
`(1)/(cos^20)` - 1

= sec²Θ - 1

= tan²Θ

Answer 2

`\tan^2(\theta)`

Explanation:

Assuming this is

`(\cos(\theta)-cos^3(\theta))/(cos^3(\theta))`

Trig identities used:

`\sin^2(\theta)+\cos^2(\theta)=1 \implies 1-\cos^2(\theta)=\sin^2(\theta)`

`(\cos(\theta)-cos^3(\theta))/(cos^3(\theta))`

`=(\cos(\theta)(1-cos^2(\theta)))/(cos^3(\theta))`

`=(1-cos^2(\theta))/(cos^2(\theta))`

`=(sin^2(\theta))/(cos^2(\theta))`

`=\tan^2(\theta)`