Verify that each equation is an identity?

Question

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

3410 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-29T19:14:10

Multiply out the brackets and then apply the Pythagorean Identity $Tan^2(x) + 1 = Sec^2(x)$

Left Side = (SecA - TanA)(SecA + TanA)
= $Sec^2A + SecATanA - TanASecA - Tan^2A$

Notice that $SecATanA - TanASecA = 0$

So Left Side = $Sec^2A - Tan^2A$

Now apply the Pythagorean Identity $Tan^2A + 1 = Sec^2A$ by replacing the $Sec^2A$ by $Tan^2A + 1$

Left Side = $Tan^2A + 1 - Tan^2A$

Left Side = 1

Left Side = Right Side [Q.E.D.]