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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

= sec (x) + 1

= 1 + sec (x)

We showed that the two sides could take the same form

\Rightarrow True

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