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

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

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

prove

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

True

Solution steps

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

Manipulating left side

(sec (x) + tan (x)) (sec (x) - tan (x))

Expand

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

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

Use the Pythagorean identity:

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

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

= 1

We showed that the two sides could take the same form

\Rightarrow True

csc (x) (sin (x) + cos (x)) = 1 + cot (x)

(1 - cos^{2} (x)) cot^{2} (x) = cos^{2} (x)

cos (6 x) = 2 cos^{2} (3 x) - 1

tan^{2} (x) - tan^{2} (x) sin^{2} (x) = sin^{2} (x)

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

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