What is (1+sec(a))(1-sec(a)) ?

The solution to (1+sec(a))(1-sec(a)) is -tan^2(a)

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simplify (1+sec(a))(1-sec(a))

simplify

(1 + sec (a)) (1 - sec (a))

- tan^{2} (a)

Solution steps

(1 + sec (a)) (1 - sec (a))

Expand

(1 + sec (a)) (1 - sec (a)) : 1 - sec^{2} (a)

= 1 - sec^{2} (a)

Use the Pythagorean identity:

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

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

= - tan^{2} (a)

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What is (1+sec(a))(1-sec(a)) ?
The solution to (1+sec(a))(1-sec(a)) is -tan^2(a)