Thread: Mathematics - Really Simple Trig Identities that I can't get!

Prove:
(tanx)(sinx) / (tanx) + (sinx) = (tanx) - (sinx) / (tanx)(sinx)

What I have so far:

L.S.
= (sinx / cosx) sinx / (sinx / cosx) + sinx
= (sin^2x / cosx) / (sinx + (sinx) (cosx) / cosx)
= (sin^2x / cosx) / (cosx / sinx + sinxcosx)

What do I do now and if I did something wrong, where did I go wrong and how should I go about to fix it?

Originally Posted by Macleef

Prove:
sin^2x - sin^4x = cos^2x - cos^4x

What I have:

L.S.
= sin^2x - sin^4x
= sin^2x (-sin^2x)
= 1 - cos^2x (-1 + cos^2x)
= -1 +cos^2x + cos^2x - cos^4x
= cos^2x - 1 +cos^2x - cos^4x
= sin^2x + cos^2x - cos^4x

Where did I go wrong?

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Originally Posted by Macleef

Prove: sinx - 1 / sinx + 1 = - cos^2x / (sinx + 1)^2

What I have so far:

R.S.
= - (1 - sin^2x) / (sinx + 1) (sinx + 1)
= -1 + sin^2x / (sinx + 1) (sinx + 1)

What do I do now?

can you continue now?
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Originally Posted by Macleef

Prove:
(tanx)(sinx) / (tanx) + (sinx) = (tanx) - (sinx) / (tanx)(sinx)

What I have so far:

L.S.
= (sinx / cosx) sinx / (sinx / cosx) + sinx
= (sin^2x / cosx) / (sinx + (sinx) (cosx) / cosx)
= (sin^2x / cosx) / (cosx / sinx + sinxcosx)

What do I do now and if I did something wrong, where did I go wrong and how should I go about to fix it?

, multiplying yields RHS..

Prove:
sin^2x - sin^4x = cos^2x - cos^4x




^^^

How did you get "sin^2x(1 - sin^2 x)" in the second line? When I did this, I got "sin^2x (-sin^2x)"
Can you tell me what I did wrong ? I don't know how you got the "1" from ...

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can you continue now?

When I did this, I get:
= (-1 + sinx) (1 + sinx) / (sinx + 1) (sinx +1)
= (-1 + sinx) / (sinx + 1)

And now I'm stumped? I don't know what to do ...

Originally Posted by Macleef

How did you get "sin^2x(1 - sin^2 x)" in the second line? When I did this, I got "sin^2x (-sin^2x)"
Can you tell me what I did wrong ? I don't know how you got the "1" from ...

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remember factoring.. (a+ab)=a(1+b), so when you factored out sin^2 x from sin^2 x - sin^4 x, it must be sin^2 x (1 - sin^2 x).. you should remain 1 from the parenthesis..

Originally Posted by Macleef

When I did this, I get:
= (-1 + sinx) (1 + sinx) / (sinx + 1) (sinx +1)
= (-1 + sinx) / (sinx + 1)

And now I'm stumped? I don't know what to do ...

you are done.. that's what you want to show right?

Originally Posted by kalagota

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remember factoring.. (a+ab)=a(1+b), so when you factored out sin^2 x from sin^2 x - sin^4 x, it must be sin^2 x (1 - sin^2 x).. you should remain 1 from the parenthesis..



you are done.. that's what you want to show right?

The first one, I remember it now, thanks

And as for the second one,

I'm proving

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

But ... when I did RS = RS, I get this:

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

Why do I have a negative in the numerator next to the bracket? How do I remove this to prove the identity?

Originally Posted by Macleef

The first one, I remember it now, thanks

And as for the second one,

I'm proving

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

But ... when I did RS = RS, I get this:

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

Why do I have a negative in the numerator next to the bracket? How do I remove this to prove the identity?

wait, did u mean like this?

or or

first, second or third?

Originally Posted by kalagota

wait, did u mean like this?

or or

first, secodn or third?

I mean like

= - (1 - sinx) over (sinx + 1)

or

- (1 - sinx)
_____________
sinx + 1

i am asking what is your left hand side.. first second or third?

coz if its the third one, then you are done with

..
remember that addition of real number is commutative so
which is the third one..

wow I see it now, thanks, I feel so stupid right now -_-