Question

tan (x) csc (x)

I need to match the above trig expression to one of the following:

sec (x), -1, cot (x), 1, -tan (x), or sin (x)

An explanation would also be great! I'm pretty sure I need to use an Identity, but I'm not sure which one.

Answer 1

do you know what is csc(x) ?

Answer 2

csc (x) is cosecant, the reciprocal of sin (x)

Answer 3

good and tan(x) ?

Answer 4

sin(x)/cos(x), right?

Answer 5

right
so what would be the multiplication of them ?

Answer 6

I'm not sure I follow the question, do you mean the product of sin and cos, or the product of tan and csc?

Answer 7

we know that tan(x) = sinx(x)/cos(x)
and csc(x) = 1/sin(x)
we need to find what is tan(x) * csc(x) = (sin(x)/cos(x)) * (1/sin(x))

Answer 8

do you know the answer now ?

Answer 9

so essentially all I need to do is simplify (sin(x)/cos(x)) * (1/sin(x))? If so, I should be able to work that out

Answer 10

yes .. in fact there is nothing much to do in this question
you only had to write tan(x) and csc(x) as the basic functions sin(x),cos(x) :)

Answer 11

Wow. It's seems so simple now! The answer is Sin(x), yes?

Answer 12

\[\frac{ \sin(x) }{ \cos(x) } * \frac{ 1 }{ \sin(x) }\]

Answer 13

are you sure ?

Answer 14

I was taught never to cancel out, so I need to cross multiply.
(Sin^2(x) cos(x))/(cos(x) sin(x))
The cosines divide out to 1, leaving me with Sin^2(x)/Sin(x), which then divides out to Sin(x)

Answer 15

Have I done anything wrong?

Answer 16

yes
seems like you treat it as an equation :
\[\frac{ sinx }{ cosx } = \frac{ 1 }{ sinx }\]
?
or i dont even understand what you did there

Answer 17

Cross multiply both Sin(x) for Sin^2(x), then cross multiply Cos(x) and 1, which is just Cos(x)
After that, you multiply the denominators, which stay on the bottom, so that gives you Cos(x) Sin(x)

The numerator comes out to be Sin^2(x) Cos(x) and the denominator comes out to be Cos(x) Sin(x), ergo (Sin^2(x) Cos(x))/(Cos(x) Sin(x))

Answer 18

but why do you think of cross multiplication
you do this when you have an equation .. this is an expression!!

Answer 19

We're multiplying two fractions though, so cross multiply, right?

Answer 20

no!

Answer 21

tell me please my friend :
\[\frac{ 1 }{ 2 } * \frac{ 6 }{ 1 }\]

Answer 22

what is the result ?

Answer 23

3

Answer 24

right .. no cross multiplication here agree?

Answer 25

OH, I see what you mean now!

Answer 26

I just did a quick redo without cross multiplying and got Sec(x)

Answer 27

there is a point anyway ..
whenever you cancel out something you have to make sure it isnt zero ..
so in fact the solution holds only if sin(x) isnt zero
which is obvious cause csc(x) wont exist if so

Answer 28

yes.. the answer is sec(x) :)

Answer 29

Thank you for walking me through this! Much appreciated!

Answer 30

yw :)