Question

Use basic identities to simplify the expression.

(1/cot^2θ) + sec θ cos θ

Answer 1

Lets focus on the right side of the expression:
sec0cos0

That is equal to:
1/cos0(cos0)

Which is equal to:
1

So now you're left with:
(1/cot^2 0) + 1

Now on the left:
1/cot^2 0

That is equal to:
1/(1/tan^20)

And you can simplify that to:
tan^20

Now you have:
tan^20 + 1

That's equal to the identity:
sec^20

Answer 2

\(=\tan^2 \theta + \sec \theta \cos \theta\)

\(=\tan^2 \theta + \dfrac{1}{\cos \theta} \cos \theta\)

\(= \tan^2 \theta + 1\)

\(= \sec^2 \theta\)