Is (sec(a)-tan(a))(sec(a)+tan(a))=1 ?

The answer to whether (sec(a)-tan(a))(sec(a)+tan(a))=1 is True

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prove (sec(a)-tan(a))(sec(a)+tan(a))=1

prove

(sec (a) - tan (a)) (sec (a) + tan (a)) = 1

True

Solution steps

(sec (a) - tan (a)) (sec (a) + tan (a)) = 1

Manipulating left side

(sec (a) - tan (a)) (sec (a) + tan (a))

Expand

(sec (a) + tan (a)) (sec (a) - tan (a)) : sec^{2} (a) - tan^{2} (a)

= sec^{2} (a) - tan^{2} (a)

Use the Pythagorean identity:

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

sec^{2} (a) - tan^{2} (a) = 1

= 1

We showed that the two sides could take the same form

\Rightarrow True

sec (x - \frac{π}{2}) = csc (x)

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

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

sin (A) = \frac{1}{csc ( A )}

\frac{9}{tan ( x )} + \frac{9}{cot ( x )} = 9 tan (x) + 9 cot (x)

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