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

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

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prove (tan^2(a)+1)/(sec(a))=sec(a)

prove

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

True

Solution steps

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

Manipulating left side

\frac{tan ^{2} ( a ) + 1}{sec ( a )}

Rewrite using trig identities

\frac{tan ^{2} ( a ) + 1}{sec ( a )}

Use the Pythagorean identity:

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

= \frac{sec ^{2} ( a )}{sec ( a )}

Cancel the common factor:

sec (a)

= sec (a)

= sec (a)

We showed that the two sides could take the same form

\Rightarrow True

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