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# Trigonometric Relationships ...help?? watch

1. Hi !

I know this should be really easy
but I just can't seem to get my head round it !!

Can anyone point me in the right direction for this question:

SIMPLIFY
tan^2x (cot^2x + 1) / tan^2x + 1

might involve use of Pythagorean identities, i'm not sure !

thanks xxx
2. Since cot is the inverse of tan we have,

cot^2x * tan^2x = 1
3. and 1 + tan^2x = sec^2x
4. (Original post by john1234567)
and 1 + tan^2x = sec^2x
This identity is not needed.

5. Thank you ever so much !!

What a lovely welcome to TSR

I've tried 1 + tan^2x = sec^2x various times but it didn't seem to cancel out nicely

xxx
6. I think you should end up with 1 as your answer
7. yeah

i think cot^2x * tan^2x = 1
hit the nail on the head ...i'm just a little confused as to how notnek managed to do it ...and so quickly !!
8. (Original post by small_fry)
yeah

i think cot^2x * tan^2x = 1
hit the nail on the head ...i'm just a little confused as to how notnek managed to do it ...and so quickly !!
Are you confused about the identity:
cot^2x * tan^2x = 1 ?

Let tan(x)=y

Then cot(x) is the reciprocal of tan(x) i.e. 1/y.

cot^2x * tan^2 x = 1/y^2 * y^2 = 1

With a bit of practice, you should be able to spot these kind of things straight away. Another one would be:

cosec(x)*sin(x)=1 or cosec^2(x)*sin^2(x)=1
9. that makes a lot of sense, and thank you ever so much for the other examples !

i feel a little bit more mathematically enlightened
10. (Original post by small_fry)
that makes a lot of sense, and thank you ever so much for the other examples !

i feel a little bit more mathematically enlightened
You're welcome.

Oh and welcome to TSR, home of the best maths help forum on the net where no question is left unanswered!

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