Question

sin(2x)cos(5x) + cos(2x)sin(5x)
use identities to simplify

Answer 1

sin(7x)

Answer 2

how did you get that?

Answer 3

sin(2x+5x)

Answer 4

remember sin(z+y)=sinzcosy+sinycosz where in this case z=2x and y=5x

Answer 5

where did the cos go?

Answer 6

its an identity

Answer 7

this is so confusing.. :(

Answer 8

do you know the identity sin(z+y)=sinzcosy+sinycosz

Answer 9

yes

Answer 10

but i don't understand how it's used in this question because sin and cos are being multiplied together.

Answer 11

ok what if you let z=2x and y=5x what would you have?

Answer 12

i understand how to use the identity, i'm just confused as to where it's being used

Answer 13

ok we have [sin(2x)][cos(5x)]+[cos(2x)][sin(2x)]=[sin(z)][cos(y)]+[cos(y)][sin(z)]=sin(y+z) where y=2x and z=5x so this =sin(2x+5x)=sin(7x)

Answer 14

oops i wrote the samething twice and that post

Answer 15

ohhh my gosh. i get it now

Answer 16

i'm so sorry. haha

Answer 17

ok good i don't have to write it over correctly then?

Answer 18

no, that is good
1 / 1-cos(x) + 1 / 1 + cos(x)

Answer 19

i assume that (1-cosx) and (1+cosx) are in the denominator right?

Answer 20

yes

Answer 21

combine those fractions

Answer 22

okay

Answer 23

what do you get now?

Answer 24

numerator=(1+cosx)+(1-cosx)=2 and denominator=1-(cosx)^2=(sinx)^2

Answer 25

2/(sinx)^2=2(cscx)^2

Answer 26

i got a denominator of 1-cos(x)1+cos(x)

Answer 27

(1-cosx)(1+cosx) use foil here

Answer 28

ohh okay

Answer 29

or you could use the fact that (a-b)(a+b)=a^2-b^2

Answer 30

we haven't learned that one, but i'll note it

Answer 31

thats an algebra thing it should had been algebra you learned that not trig

Answer 32

hmm, i don't remember it thankyou though.

Answer 33

(x-3)(x+3)=x^2-9 and (x-5)(x+5)=x^2-25 and so on....

Answer 34

\[\tan(\pi/5) + \tan(\pi/10) = numerator. 1 - \tan(\pi/5)\tan(\pi/10)\]

Answer 35

sorry. let me re-write that

Answer 36

what you got the one before this one?

Answer 37

numerator = tan(pi/5) + tan(pi/10)
denominator = 1 - tan(pi/5)tan(pi/10)

Answer 38

yes, i understood it.

Answer 39

Nice!

Answer 40

Do you remember the idenity tan(x+y)=[tanx+tany]/[1-tanxtany]

Answer 41

yes

Answer 42

can use that here?

Answer 43

x=pi/5 and y=pi/10

Answer 44

3pi / 10?

Answer 45

tan 3pi/10, i mean

Answer 46

yes!!! :))

Answer 47

ok if you want more help, i'm gonna be away from my computer so people will notice you you might want to start a new thread k? if you like me become a fan

Answer 48

okay