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

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

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

prove

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

True

Solution steps

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

Manipulating left side

\frac{sec ( θ )}{sec ( θ ) - 1}

Express with sin, cos

= \frac{1}{1 - cos ( θ )}

We showed that the two sides could take the same form

\Rightarrow True

2 cos (θ) - \frac{cos ( 2 θ )}{cos ( θ )} = sec (θ)

cos (2 \cdot 30) = cos^{2} (30) - sin^{2} (30)

1 + tan^{2} (4 5^{\circ}) = sec^{2} (4 5^{\circ})

\frac{cot ( x )}{cos ( x )} = csc (x)

\frac{sin ( x ) cos ( x )}{tan ( x )} = cos^{2} (x)

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