Question

Simplify the expression sec(u) csc(u)-sec(u)sin(u) as a single trigonometric function.

Answer 1

( sec u)(csc u)-(sec u)(sin u)?

Answer 2

When in doubt, it's always smart to just convert everything to sin's and cos's first.

Answer 3

(1/cos u)(1 sin u)-(1/cos u)(sin u)

Answer 4

1/ sin u

Answer 5

-.-

Answer 6

(1/ cos u)(1/ sin u)-(1/cos u)(sin u)

Answer 7

cot=cos/sin?

Answer 8

do you mean 1/cot u?

Answer 9

you're on the right track there, luiz, now get everything over a common denominator

Answer 10

what on the right side?

Answer 11

sin u/cos u=tan u

Answer 12

on the right side

Answer 13

so wait

Answer 14

you still there bang?

Answer 15

ok, (1/cos u)(1/ sin u)- (1/cos u)(sin u)

Answer 16

I got that part

Answer 17

any tips or hints?

Answer 18

I got (1/cos u)(1/ sin u)- (1/cos u)(sin u)

Answer 19

so...

Answer 20

hmm

Answer 21

you still there?

Answer 22

hey Happyfeet?

Answer 23

hey, still need help?

Answer 24

I'm sorry, but I'm still having trouble and yes I still need help lol

Answer 25

I saw many people helped you so I let them do. but at the end.. ha!!!

Answer 26

I got (1/cos u)(1/ sin u)-(1/cos u)(sin u)

Answer 27

wat next?

Answer 28

ok, back to the original one. first off factor sec out.

Answer 29

show me your work, please, follow my guide

Answer 30

so...

Answer 31

factor sec out, what do you have?

Answer 32

sec u(1 times 1/sin u)- sec u(1 times sin u)

Answer 33

it's not the way to factor
\[\large sec (u) csc (u) - sec (u)sin(u) = sec (u) [css (u) - sin (u)]\]
get it?

Answer 34

ahh

Answer 35

so wait

Answer 36

I got that part

Answer 37

you see it, right? you can step up from there, right?

Answer 38

so wait, lol

Answer 39

hahaha.. .ok, I am waiting, my friend, take time, manipulate the part [ ]

Answer 40

ok

Answer 41

so

Answer 42

sec bracket 1-sin squared u/sin u bracket?

Answer 43

so sec bracket cos squared u/sin u bracket?

Answer 44

\[sec(u) [ csc (u) - sin (u)]\] and replace \(csc (u) = \dfrac{1}{sin (u)}\) into the bracket, you have
\[sec(u) [ \frac{1}{sin(u)}-sin(u)]\] still manipulatate the term in the bracket [ ]
make them have the same denominator
\[sec(u) [ \frac{1 -sin^2(u)}{sin(u)}]\]
get this part?

Answer 45

yes, lord happyfeet

Answer 46

now replace \(1 - sin^2(u) = cos^2(u) to the numerator you have