Question

Trigonometry help

Multiply and Simplify

sinx cosx (cscx + tanx)=

Please show me how to solve this, I've been struggling with this.

Answer 1

I can help!

Answer 2

Awesome! Please do!

Answer 3

First tell me what csc is the cofunction for.

Answer 4

like 1\sin x?

Answer 5

Then do the same with tangent. Do you know what I mean by that?

Answer 6

and tan is sinx\cosx?

Answer 7

Yes to both!

Answer 8

so let's rewrite our expression using those identities instead:

Answer 9

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

Answer 10

I have gotten as far as:
sinx cosx \[\frac{ 1 }{ sinx }\] + sinx cosx \[\frac{ sinx }{ cosx }\]

Answer 11

i cant get it to type on one line but that

Answer 12

Now you have to distribute the sin(x)cos(x) into the parenthesis like this:

Answer 13

\[\frac{ \sin(x)\cos(x) }{ \sin(x) }+\frac{ \sin ^{2}(x)\cos(x) }{ \cos(x) }\]

Answer 14

Now let's find a common denominator between the two:

Answer 15

I got something different from you...let me check mine and look at yours as well, ok?

Answer 16

mine is probably wrong but alright, thanks.

Answer 17

Don't say that...we all make oversights of important stuff...I did it twice today!

Answer 18

lol thanks

Answer 19

I got the same thing both times I checked so here's how I did it and see if you can follow my step by step, ok?

Answer 20

alright

Answer 21

We already established that csc = 1/sin and tan = sin/cos so I will go straight to the next part:

Answer 22

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

Answer 23

We will distribute the sin(x)cos(x) into the parenthesis to get this:

Answer 24

...\[\frac{ \sin(x)\cos(x) }{ \sin(x)}+\frac{ \sin ^{2}(x)\cos(x) }{ \cos(x) }\]

Answer 25

ok got that part

Answer 26

Now we need to put those over a common denominator. Do this by multiplying the first part of the expression by cos(x)/cos(x) and the second part by sin(x)/sin(x):

Answer 27

fingers crossed, hope i did it right :D