Question

Use basic identities to simplify the expression.

Answer 1

Convert each of the three trig functions to sin and cos.

Answer 2

How do I do that? I don't really understand how to work with identities in the 1st place.

Answer 3

\[\sec \theta=\frac{ 1 }{ \cos \theta }\]
etc.

Answer 4

Okay so cscu=1/sinu
cot=cosu/sinu

Answer 5

yes
$$\bf
\frac{csc(\theta)cot(\theta)}{sec(\theta)}\\
\large \cfrac{
\frac{1}{sin(\theta)}\frac{cos(\theta)}{sin(\theta)}
}{
\frac{1}{cos(\theta)}
}
\implies
\cfrac{
\frac{cos(\theta)}{sin^2(\theta)}
}{
\frac{1}{cos(\theta)}
}\\
\text{now keep in mind that}\\
\cfrac{\frac{a}{b}}{\frac{c}{d}} \implies \frac{a}{b} \times \frac{d}{c}
$$

Answer 6

thus \(\bf \large \cfrac{
\frac{cos(\theta)}{sin^2(\theta)}
}{
\frac{1}{cos(\theta)}
}
\implies \frac{cos(\theta)}{sin^2(\theta)} \times
\frac{cos(\theta)}{1}\)

Answer 7

so, what would that give you?

Answer 8

csc2u? Omg I don't really know. I'm trying to follow it but the last part is throwing me off. I don't understand how you'd multiply it out to get one of the choices from above.

Answer 9

hmmm, what part confused you?

Answer 10

The final step before getting the final answer after rearranging the equation and doing a/b*d/c.

Answer 11

yes anything wrong with \(\bf \huge \cfrac{\frac{a}{b}}{\frac{c}{d}} \implies \frac{a}{b} \times \frac{d}{c}\ \ ?\)

Answer 12

my 2 fractions were \(\bf \large \cfrac{
\frac{cos(\theta)}{sin^2(\theta)}
}{
\frac{1}{cos(\theta)}
}\)
thus

Answer 13

No I understood that. It's: cos(θ)sin2(θ)×cos(θ)1

Is it cos2u/sin2u which means it's sec2u?

I'm not sure how to multiply that part out is what I meant.

Answer 14

Whoops cosu/sin2u*cosu/1 not cos(θ)sin2(θ)×cos(θ)1

Answer 15

hmm, multiplication of rationals is just across the board
numerator by numerator and denominator by denominator

Answer 16

Yeah I got cos2u/sin2u which doesn't fit the choices:
sec2u, cot2u, csc2u, and 1

Answer 17

hmm well, we haven't multiplied across yet :)

Answer 18

$$\bf \cfrac{
\frac{cos(\theta)}{sin^2(\theta)}
}{
\frac{1}{cos(\theta)}
}
\implies \cfrac{cos(\theta)}{sin^2(\theta)} \times
\cfrac{cos(\theta)}{1} \implies
\cfrac{cos^2(\theta)}{sin^2(\theta)}
$$

Answer 19

so as you said =>\(\text{Okay so cscu=1/sinu } \\
\bf \text{cot=cosu/sinu}\)

so what do you think you'd simplify the rational to?

Answer 20

cot2u

Answer 21

\(\bf \cfrac{cos^2(\theta)}{sin^2(\theta)} \implies cot^2(\theta)\)

Answer 22

Yayy! Thanks so much for having the time and patience to put up with me! I actually grasp the concept much better now. :O

Answer 23

yw