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

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

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

prove

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

True

Solution steps

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

Manipulating left side

\frac{tan ^{2} ( x )}{sec ( x ) - 1}

Rewrite using trig identities

= sec (x) + 1

Express with sin, cos

= \frac{1 + cos ( x )}{cos ( x )}

Expand

\frac{1 + cos ( x )}{cos ( x )} : \frac{1}{cos ( x )} + 1

= 1 + \frac{1}{cos ( x )}

We showed that the two sides could take the same form

\Rightarrow True

cos (α + β) - cos (α - β) = - 2 sin (α) cos (β)

\frac{cot ( x )}{sin ( x )} = 1

7 sec (θ) = \frac{7 sec ( θ ) - 7}{1 - cos ( θ )}

2 tan (x) sin (x) - 3 cos (x) = 2

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

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