Question

Can someone help me simplify this trig expression???............sec(x)cot(x)-cot(x)cos(x)

Answer 1

sec cot-cot cos

sub in sec = 1/cos, and cot = 1/tan = cos/sin

Answer 2

yeah i did so but its confusing me

Answer 3

sec cot - cot cos

= (1/cos)(cos/sin) - (cos/sin)cos
now simplify
=

Answer 4

(1/cosx)(cosx/sinx)-(cosx/sinx * cosx)

Answer 5

right, now simplify

Answer 6

yeah thats where im stumped

Answer 7

the first term is
(1/cosx)(cosx/sinx)

cancel the cosines

Answer 8

1/sinx ?

Answer 9

yeah,

now simplify (cosx/sinx * cosx)

Answer 10

cos^2x/sinx ?

Answer 11

good, so you have

1/sinx - cos^2x/sinx ?

now factor out the 1/sin

Answer 12

umm

Answer 13

1-cos^2x/sinx

Answer 14

so it's sinx?

Answer 15

yeah
(1-cos^2x)/sinx

now use sin^2+cos^2=1 i.e. 1-cos^2 = sin^2

Answer 16

yes!

Answer 17

cool. one more??

Answer 18

ok

Answer 19

cosx/1+sinx + cosx/1-sinx

Answer 20

is that meant to be

cosx/(1+sinx) + cosx/(1-sinx) ?

Answer 21

yeah

Answer 22

change the first term by multiplying by 1 = (1-sinx)/(1-sinx)

cosx/(1+sinx)

= cosx/(1+sinx) * (1-sinx)/(1-sinx)

Answer 23

i dont know where to start

Answer 24

cosx/(1+sinx)

= cosx/(1+sinx) * (1-sinx)/(1-sinx)

= cosx(1-sinx) / (1-sin^2x)

Answer 25

now do something similar to the second term:

multiply cosx/(1-sinx) by 1 = (1+sinx)/(1+sinx)

Answer 26

ok

Answer 27

cos(1-sinx)/1-sin^2x

Answer 28

not quite

cos(1+sinx)/(1-sin^2x)

Answer 29

oh my bad thats what i had

Answer 30

i got 2cosx/cos^2x

Answer 31

so you have
cosx/(1+sinx) + cosx/(1-sinx)

= cosx(1-sinx) / (1-sin^2x) + cos(1+sinx)/(1-sin^2x)

now the denominator are the same , we can add the terms

Answer 32

2cosx/cos^2x is right,

now just simplify a little bit

Answer 33

i dont know how to simplify that

Answer 34

you have 2cosx/cos^2x

if we imagine that cosx = z

you have 2z/z^2

Answer 35

cancel a factor of z (cosine)

Answer 36

2cosx??

Answer 37

almost, try again

Answer 38

2cos?

Answer 39

no

Answer 40

sorry its late...real late

Answer 41

cosx

Answer 42

2z/z^2 = 2/z

Answer 43

2/cosx?

Answer 44

yes, but you can simplify further still

Answer 45

hmmm

Answer 46

sec

Answer 47

2secx

Answer 48

the 2 is kept?

Answer 49

yes,

Answer 50

cosx=1/secx right?

Answer 51

that is right

Answer 52

so its just replacing the 1 with a 2?

Answer 53

you had 2 / cos x

using 1/ cos x = sec x

we get 2sec x

Answer 54

all right one quick question.... if i had cos^4x/sin^2x would it simplify to cot^2x?

Answer 55

cos^4x / sin^2x

= cos^2x * cos^2x / sin^2x

= cos^2x * cot^2

Answer 56

ok thanks a lot!!!