Is (cos^2(x)-1)/(cos(x)-1)=cos(x)+1 ?

The answer to whether (cos^2(x)-1)/(cos(x)-1)=cos(x)+1 is True

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prove (cos^2(x)-1)/(cos(x)-1)=cos(x)+1

prove

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

True

Solution steps

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

Manipulating left side

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

Simplify

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

= 1 + cos (x)

= cos (x) + 1

We showed that the two sides could take the same form

\Rightarrow True

cosh^{(2)} (x) - sinh^{(2)} (x) = 1

sin (2 x) - cos (2 x) = 1 - 2 cos (2 x)

cot^{2} (x) tan (x) sin (x) = cos (x)

tan (x) (csc^{(2)} (x) - 1) = cot (x)

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

Is (cos^2(x)-1)/(cos(x)-1)=cos(x)+1 ?
The answer to whether (cos^2(x)-1)/(cos(x)-1)=cos(x)+1 is True