Is (1-cos(x))/(-1+1/(cos(x)))=cos(x) ?

The answer to whether (1-cos(x))/(-1+1/(cos(x)))=cos(x) is True

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prove (1-cos(x))/(-1+1/(cos(x)))=cos(x)

prove

\frac{1 - cos ( x )}{- 1 + \frac{1}{c o s ( x )}} = cos (x)

True

Solution steps

\frac{1 - cos ( x )}{- 1 + \frac{1}{c o s ( x )}} = cos (x)

Manipulating left side

\frac{1 - cos ( x )}{- 1 + \frac{1}{c o s ( x )}}

Simplify

\frac{1 - cos ( x )}{- 1 + \frac{1}{c o s ( x )}} : cos (x)

= cos (x)

We showed that the two sides could take the same form

\Rightarrow True

cos^{4} (x) - sin^{4} (x) = tan^{2} (x)

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

cos (a) = 2 cos^{2} (\frac{a}{2}) - 1

tan^{3} (x) = \frac{sin ^{3} ( x )}{cos ^{3} ( x )}

cos (4 θ) = 1 - 8 sin^{2} (θ) cos^{2} (θ)

Is (1-cos(x))/(-1+1/(cos(x)))=cos(x) ?
The answer to whether (1-cos(x))/(-1+1/(cos(x)))=cos(x) is True