Question

Complete the following identity. ________?=sec^2 θ (Multiple Choice)

Answer 1

A. tan^2 θ+1

B.tan^2θ-1

C.1+cot^2 θ

D.1-cot^2 θ

Answer 2

A

Answer 3

Can you show me how to work that out?

Answer 4

Start with the pythagorean identity (step 1). Then divide both sides by cos^2(theta) (step 2).
On step 3, you'll break up the fraction. Then on step 4, you use these identities
tan = sin/cos
sec = 1/cos
x/x = 1 where x is anything but zero


So doing all that means we have these steps...


\[\Large \sin^2(\theta)+\cos^2(\theta) = 1\]

\[\Large \frac{\sin^2(\theta)+\cos^2(\theta)}{\cos^2(\theta)} = \frac{1}{\cos^2(\theta)}\]

\[\Large \frac{\sin^2(\theta)}{\cos^2(\theta)}+\frac{\cos^2(\theta)}{\cos^2(\theta)} = \frac{1}{\cos^2(\theta)}\]

\[\Large \tan^2(\theta)+1 = \sec^2(\theta)\]

Answer 5

you can also work those problems out but you can memorize them too