Question

Use fundamental identities to simplify the expression below and then determine which of the following is NOT equivalent

cotβsecβ

answer choices:
1/sinβ
secβ/tanβ
1/(cosβtanβ)
secβ
cscβ

Answer 1

I know the answer is not cscβ

Answer 2

well, cot = cos/sin
and , sec = 1/cos

so multiply them :)

Answer 3

\(\bf \cfrac{\cancel{cos(x)}}{sin(x)}\cfrac{1}{\cancel{cos(x)}}\)

Answer 4

If \(\csc\beta\) isn't an answer, then you also know that \(\dfrac{1}{\sin\beta}\) isn't an answer, either.

Answer 5

secβ/tanβ then?

Answer 6

Nope,\[\cot\beta\sec\beta=\frac{1}{\tan\beta}{\sec\beta}=\frac{\sec\beta}{\tan\beta}\]

Answer 7

ok then 1/(cosβtanβ)? because secβ is actually in the problem

Answer 8

If you rewrite the secant in my last comment, you'll see that they're the same:
\[\frac{\sec\beta}{\tan\beta}=\frac{\frac{1}{\cos\beta}}{\tan\beta}=\frac{1}{\cos\beta\tan\beta}\]
So you've eliminated four of the answers, meaning the right answer is...

Answer 9

ha ok secβ, sorry for my stupidity but thanks for help!

Answer 10

You're welcome!