Question

establish the identity
(secθ+tanθ)(secθ−tanθ)=1
multiply and write the left side expression as the difference of two squares.
the expression from the previous step is equivalent to 1 using what?
a. even - odd identity
b. reciprocal identity
c. cancellation property
d. quotient identity
e. pythagorean identity

Explanation:

Step1: Expand the left - hand side

Using the formula \((a + b)(a - b)=a^{2}-b^{2}\), where \(a = \sec\theta\) and \(b=\tan\theta\), we get \((\sec\theta+\tan\theta)(\sec\theta - \tan\theta)=\sec^{2}\theta-\tan^{2}\theta\)

Step2: Apply the Pythagorean identity

We know the Pythagorean identity \(1+\tan^{2}\theta=\sec^{2}\theta\), which can be rewritten as \(\sec^{2}\theta-\tan^{2}\theta = 1\)

Answer:

E. Pythagorean Identity