# Thread: Trig Identities

1. ## Trig Identities

I am not understanding at all how to do the trigonometric identities...
As far as i know we had 12 of them that we had to memorize, even after memorizing them i am unsure of how to apply them.

so for my first question the problem says
(sinx + cosx)(sinx + cosx) -1 / sinxcosx
multiply and simplify
the answer is 2 however im unsure how you get that answer.

also there is

1 + tan^2(-x) = sec^2(x)
how do I get both sides to equal the same im suppose to use the more complicated side, but, which identity do I use?
If there is any easy way to remember the identities and to apply them that would be great..

2. $\displaystyle \frac{(\sin{x}+\cos{x})^2 - 1}{\sin{x}\cos{x}} =$

$\displaystyle \frac{\sin^2{x} + 2\sin{x}\cos{x} + \cos^2{x} - 1}{\sin{x}\cos{x}}$

now ... what do you know about the sum $\displaystyle \sin^2{x} + \cos^2{x}$ ?

$\displaystyle 1 + \tan^2(-x) = \sec^2(x)$

note that $\displaystyle \tan^2(x) = [\tan(x)]^2$ and that $\displaystyle \tan(-x) = -\tan(x)$

3. sin^2x+cos^2x = 1, so
1 + 2 -1 = 2 oo.....

ok and then

1 + tan x^2

1 + tan x^2 = sec x^2
oo.... thanks

ok I understand it when someone tells me what to do, but i cant think of what to use when i have to do it all alone :S

so i have 2 more problems

tanx + cosx /1+sinx = secx

so er...
sinx/cosx + cosx/1+sinx = secx
is that correct? where do i go after that? :/

also

sinx/sinx - cosx = 1 /1 - cotx

is there any way of really knowing what you have to use? still confused alot thank you

4. anyone?