Is (cos(θ))/(cos(θ)-1)= 1/(1-sec(θ)) ?

The answer to whether (cos(θ))/(cos(θ)-1)= 1/(1-sec(θ)) is True

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prove (cos(θ))/(cos(θ)-1)= 1/(1-sec(θ))

prove

\frac{cos ( θ )}{cos ( θ ) - 1} = \frac{1}{1 - sec ( θ )}

True

Solution steps

\frac{cos ( θ )}{cos ( θ ) - 1} = \frac{1}{1 - sec ( θ )}

Manipulating right side

\frac{1}{1 - sec ( θ )}

Express with sin, cos

= \frac{cos ( θ )}{- 1 + cos ( θ )}

= \frac{cos ( θ )}{cos ( θ ) - 1}

We showed that the two sides could take the same form

\Rightarrow True

cos (- \frac{π}{4} - 5 t) = cos (5 t + \frac{π}{4})

tan (\frac{π}{4} - θ) = \frac{1 - tan ( θ )}{1 + tan ( θ )}

\frac{sin ( θ )}{cot ( θ ) + csc ( θ )} = 1 - cos (θ)

csc^{2} (x) cos^{2} (x) = cot^{2} (x)

1 + cos (x) = \frac{( sin ^{2} ( x ) )}{1 - cos ( x )}

Is (cos(θ))/(cos(θ)-1)= 1/(1-sec(θ)) ?
The answer to whether (cos(θ))/(cos(θ)-1)= 1/(1-sec(θ)) is True