I need help verifying that these two expressions are equal (getting one side of the equation to look like the other without using properties of equality, just trig identities and simplifying one side).

Thanks.

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- October 8th 2009, 07:20 PMrebelspartanEstablish the trig identity

I need help verifying that these two expressions are equal (getting one side of the equation to look like the other without using properties of equality, just trig identities and simplifying one side).

Thanks. - October 8th 2009, 09:31 PMGrandad
Hello rebelspartan

Welcome to Math Help Forum!Three things you need here:

- (1)

- (2)

- (3)

So:

- Express the denominator (of the LHS) as , and then use (1) to express in terms of
- Use (3) to factorise the denominator
- Cancel (simplify) the whole fraction
- Use (2) on the remaining term in

... and you're there.

Can you do that?

Grandad - October 8th 2009, 09:42 PMrebelspartan
Great, I got it! Thanks!

- October 9th 2009, 12:00 AMpacman
http://www.mathhelpforum.com/math-he...c64ea8b5-1.gif

rebelspartan, this is less rigorous but, what if we cross multiply? let t = theta

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(sec t - i)(sec t + 1) = cot t tan^3 t = (1/tan t)(tan t)(tan^2 t), that red thing cancels out.

the LHS is the difference of 2 squares, (sec t - 1)(sec t + 1) = sec^2 t - 1

LHS = RHS, indeed sec^2 t - 1 = tan^2 t,

remember this PYTHAGOREAN IDENTITY: tan^2 t + 1 = sec^2 t - October 9th 2009, 12:27 AMGrandad
Hello everyoneVery bad style! Don't start off by assuming the thing you want to prove, and end up proving something that is known to be true. This is completely the wrong way round!

Having said that, if you can do this, then you should be able to 'reverse-engineer' your proof so that it all reads in the right direction and is therefore mathematically sound.

Grandad - October 9th 2009, 12:57 AMpacman
i agree with you grandad, my above computation is really mathematically unsound, because i assumed it already as an identity, but i experimented with it by hindsight . . . . and it works.

http://www.mathhelpforum.com/math-he...c64ea8b5-1.gif,

**formal Proof:**

Consider the RHS, that is (cot t)/(sec t + 1) only

multiply and divide by (sec t - 1)

(cot t)/(sec t + 1) = [(cot t)/(sec t + 1)][(sec t - 1)/(sec t - 1)],

use the identity: 1 + tan^2 t = sec^2 t and simplify,

(cot t)/(sec t + 1) = (cot t)(sec t - 1)/(sec^2 t - 1)

(cot t)/(sec t + 1) = (cot t)(sec t - 1)/(tan^2 t)

(cot t)/(sec t + 1) = (cot t)(sec t - 1)/(tan^2 t)

(cot t)/(sec t + 1) = (1/tan t)(sec t - 1)/(tan^2 t)

(cot t)/(sec t + 1) = (sec t - 1)/[(tan t)(tan^2 t)]

(cot t)/(sec t + 1) = (sec t - 1)/(tan^3 t) = LHS.

- - October 9th 2009, 05:19 AMGrandad
Hello pacman

That's much better!

Grandad