Verify that each equation is an identity?

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

1 Answer
Nov 29, 2016

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

Explanation:

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.]