Question

Verify the identity (1 + tan^2u)(1 - sin^2u) =

Answer 1

Seriously need help please I need a thorough explanation of how this will look cause I'm extremely lost :(

Answer 2

@Hero

Answer 3

@dan815

Answer 4

use your trig identies sin^2x+cos^2x=1
tan = sin/cos

Answer 5

can you walk me through it

Answer 6

no my son ned me 2 taqke him to the school...

Answer 7

ohh ok :/

Answer 8

just an fyi, u didnt even include the right hand side of the identity

Answer 9

that's all I was given

Answer 10

it is not an identity as there is nothing on the right hand side to verify the left hand side

Answer 11

oh, I figured we were proving an equality.


again this is just identity manipulation. it's algebra

Answer 12

@bibby @amorfide sorry its actually (1 + tan2u)(1 - sin2u) = 1

Answer 13

\[(1+\tan^{2}u)(1-\sin^{2}u)=1\]

Answer 14

and the 2s are powers

Answer 15

is this your question?

Answer 16

http://puu.sh/gSMnF.png

Answer 17

yes amor

Answer 18

well you know that
\[\tan(u)=\frac{ \sin(u) }{ \cos(u) }\]

from
\[\sin^{2}(u)+\cos^{2}(u)=1\]
we know that
\[1-\sin^{2}(u)=\cos^{2}(u)\]

Answer 19

so we can work out
\[\tan^{2}(u)=\frac{ \sin^{2}(y) }{ \cos^{2}(u) }\]

Answer 20

so replace tan squared
replace 1-sin squared

Answer 21

multiply out of the brackets

Answer 22

and you can work it out from that I am sure

Answer 23

let me know if you still need help after doing this

Answer 24

so the explanation so far is
tan^2(u)= sin^2(u)/cos^2(u)
which changes the equation to
(1+sin^2(u)/co^2(u))*(cos^2(u)=1

Answer 25

yes

Answer 26

now multiply out of the brackets and you can simplify

Answer 27

and that's now verified?

Answer 28

you will end up with
\[\cos^{2}(u)+\sin^{2}(u)=1\]

which is true since that is also an identity

Answer 29

that is now verified since left hand side is the same as the right hand side

Answer 30

let me know if you do not understand something

Answer 31

isn't that the same equation as you get to use for 1-sin^2(u)

Answer 32

you use the trig identity for \[\sin^{2}z+\cos^{2}x=1\] to work out equivalent expressions for the ones in your question, and it just happens to come out as the trig identity we all know and love

it does not always work out that way though

Answer 33

so can you explain how you broke down (1+sin^2(u)/cos^2(u)) * (cos^2(u) into sin^2(u)+cos^2(u)=1

Answer 34

that should be a plus my bad

Answer 35

im going to take a smoke so ill be back in 2 minutes or so if you don't mind

Answer 36

\[(1+\frac{ \sin^{2}(u) }{ \cos^{2}(u) })(\cos^{2}(u))\]

Answer 37

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

Answer 38

\[\frac{ \cos^{2}(u) }{ \cos^{2}(u) }=1\]

Answer 39

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

Answer 40

so this is our left hand side, and we know the right hand side is 1

Answer 41

using the trig identity
\[\cos^{2}(u)+\sin^{2}(u)=1\]

we have
1=1

Answer 42

can you explain your transition from cos^2(u)+sin^2(u) cos^2(u)/cos 2 (u) to cos^2(u)/cos^2(u)=1

Answer 43

\[\cos^{2}(u)+ \frac{\sin^{2}(u) \cos^{2}(u) }{ \cos^{2}(u) }\] this is what i had

Answer 44

there was no transition

Answer 45

i was showing that the fraction cancels out to just sin squared

Answer 46

because anything divided by itself is 1
so it was the same as sin^2(u) times 1

Answer 47

ohhhh

Answer 48

@amorfide one last thing what happened to the 1+

Answer 49

what do you mean

Answer 50

we multiplied by cos squared remember

Answer 51

(1+sin^2(u)/cos^2(u)) where did the +1 in this go

Answer 52

@amorfide

Answer 53

you missed out the other half of your trig

you had two brackets to start with
(1+tan^2(u))(1-sin^2(u))

1+tan^2(u) = 1+ sin^2(u)/cos^2(u)

1-sin^2(u)= cos^2(u)

we multiply them together

(1+sin^2(u)/cos^2(u)) x (cos^2(u))
multiply everything in the first bracket by cos^2(u)

Answer 54

ohh I tryied to do that wrong I get it now I was tryin to combine the two sides of the equation cause im stupid

Answer 55

(1+tan^2 u)(1-sin^2 u)=
(sec^2u)(cos^2)=
(1/cos^2)(cos^2u)=1

Answer 56

1+tan^2u = sec^2 u
1-sin^2= cos^2
sec^2=1/cos^2