Question

Use basic identities to simplify the expression
[csc(θ) x cot(θ)]/sec(θ)

Answer 1

What's the question?

Answer 2

what do you want????

Answer 3

Use basic identities to simplify the expression

Answer 4

ok,

What are the definition of the following:

csc(x) = ?
cot(x) = ?
sec(x) = ?

Answer 5

csc = 1/sin
cot = 1/tan
sec = 1/cos

Answer 6

substitute those^^ in the problem

Answer 7

put all in terms of sin and cos and then simplify

Answer 8

but only work with one side

Answer 9

here there is only one side......it just has to be simplified

Answer 10

Your original express now becomes
\[\frac{ \frac{ 1 }{ \sin(x) }\frac{ 1 }{ \tan(x) } }{ \frac{ 1 }{ \cos(x) } }\] can you simplify it any further? What is the definition of tan(x)?

Answer 11

so (1/sin) x (cos/1)=cos/sin
(1/tan) x (cos/1)=cos/tan
tan = sin/cos

Answer 12

[csc(θ) x cot(θ)]/sec(θ)
\[\frac{ \frac{ 1 }{ \sin \theta }*\frac{ \cos \theta }{ \sin \theta } }{ \frac{ 1 }{ \cos } }\]

Answer 13

then this gives\[\frac{ \frac{ \cos \theta }{ \sin ^{2}\theta } }{ \frac{ 1 }{ \cos \theta }}\]

further
\[\frac{ \cos \theta }{ \sin ^{2}\theta }*\frac{ \cos \theta }{ 1 }

Answer 14

Excuse me Harkirat, but I don't understand what you are saying with the whole \[\frac{ \frac{ 1 }{ . How do I interpret that?

Answer 15

sorry, it did not come out right....\[\frac{ \cos \theta }{ \sin ^{2}\theta }*\frac{ \cos \theta }{ 1 }\]
now resolve this to get your answer

Answer 16

Going off of what @Harkirat said, we just need to calculate
\[\frac{ \frac{ \cos(\theta) }{\sin ^{2}(\theta) }} { \frac{ 1 }{ \cos(\theta) } } = \frac{ \cos(\theta) }{\sin ^{2}(\theta) } \frac{ \cos(\theta) }{ 1 } = \frac{ \cos ^{2}(\theta) }{ \sin ^{2}(\theta) }\]

Answer 17

Finally
\[\frac{ \cos ^{2}\theta }{ \sin ^{2}\theta }=\left( \frac{ \cos \theta }{ \sin \theta } \right)^{2}=\cot ^{2}\]

Answer 18

I'm confused

Answer 19

what part confuses you???

Answer 20

Do I have this right?