Question

Verify the identity.

tan x + (pi/2)= -cot x

Answer 1

tan(x+(pi/2))=-cot(x) ?

Answer 2

yes

Answer 3

You could use that tan(t)=sin(t)/cos(t)
then use the sum identity for sine and cosine

Answer 4

i know the identities but i'm not sure how to solve it

Answer 5

This has to do with phase shifts:
\[\sin(x+\frac{\pi}{2}) = \cos(x)\]
\[\cos(x+\frac{\pi}{2}) = -\sin(x)\]
The two shifts above can help you prove your identity.

Answer 6

I've always hated memorizing stupid pointless "shortcuts" for trigonometry, so here's the easiest way to do it in my opinion.

All you need to know is what the common values of sin and cos are (for 0,30,60,90,180 degrees) and sin(a+b) with cos(a+b) and you've pretty much slashed through 80% of things some teachers might insist that you need to memorize.

Answer 7

\[\frac{\sin(x+\frac{\pi}{2})}{\cos(x+\frac{\pi}{2})}\]
use the sum identity for both sin and co

Answer 8

Go to the definition of tan:

tan(x) = sin(x)/cos(x)

So if you have tan(a+b) it's sin(a+b)/cos(a+b).

Answer 9

Now instead of b you have pi/2.

Replace sin(x+b) with sin(x+pi/2) which is sin(x)*cos(pi/2)-sin(pi/2)*cos(x).
Since cos(pi/2) (or cos(90), whatever you prefer) is 0, the above thing equals -cos(x).

Do the same for cos(x+pi/2) and you'll get sin(x).

Answer 10

okay, i think i understand. thanks all!

Answer 11

can anyone help with this problem too? it's my last one

Verify the identity.

(1- sin x)/(cos x) = (cos x)/(1+ sin x)

Answer 12

do i cross multiply?

Answer 13

@AngusV

Answer 14

If you cross multiply you'll see that you get to the fundamental equation of trigonoetry - the one with:

sin(x)^2+cos(x)^2=1.

So just reverse engineer it a bit.

Answer 15

\[\frac{1-\sin(x)}{\cos(x)} \cdot \frac{1+\sin(x)}{1+\sin(x)}\]
multiply top and bottom by top's conjugate for the left hand side expression

Answer 16

I don't think you can move something over from one side to another when proving something is something else

Answer 17

that is you can take the left hand side and show it is the same as the right hand side
or you can take the right hand side and show it is the left hand side

Answer 18

okay, and then what would i do? i'm still lost

Answer 19

have you tried doing what i suggest above

Answer 20

\[\frac{1-\sin(x)}{\cos(x)} \cdot \frac{1+\sin(x)}{1+\sin(x)}=?\]