Question

Verify the Identity. tan(x+pi/2)=-cot x

Answer 1

do you know the formula for tan (A+B)?

Answer 2

yes

Answer 3

use it. sub x for A and pi/2 for B

Answer 4

remember that sin(pi/2) = 1 and cos(pi/2) = 0

Answer 5

tan (a+b)=sin (a+b)/cos(a+b)

Answer 6

?

Answer 7

Yes, and don't forget also the identities for sin(a+b) and cos(a+b)
Like
sin(a+b) = sin(a)cos(b) + cos(a)sin(b)
cos(a+b) = cos(a)cos(b) - sin(a)sin(b)

Answer 8

i think i remember it as \[\frac{\tan A + \tan B}{1 + \tan A\tan B}\]
or something like that

Answer 9

maybe i'm wrong

Answer 10

Can't, @abb50 because...
What will you do about
\[\Large \tan \frac\pi 2=\color{red}?\]

Answer 11

interesting point

Answer 12

I know that tan(x-pi/2)=cot but i dont know how to get to it

Answer 13

Plug it in here...
\[\Large \tan \left(x + \frac \pi 2\right)= \frac{\sin \left(x + \frac \pi 2\right)}{\cos \left(x + \frac \pi 2\right)}\]

Answer 14

I still dont understand

Answer 15

since a 99 SS user has come, I suppose I'll take my leave now

Answer 16

No, by all means, carry on, @abb50 if you like :)

Answer 17

Maybe you can try to convert \(-cot(x)\) to\(\frac{ -1 }{ \tan(x) }\), then use the \(\tan(a+b)\)formula to figure out what the left side is.

Answer 18

$$
\Large \tan \left(x + \frac \pi 2\right)= \frac{\sin \left(x + \frac \pi 2\right)}{\cos \left(x + \frac \pi 2\right)} \implies \frac{cos(x)}{-sin(x)}
$$

Answer 19

@terenzreignz is not a 99 SS (at least not yet) he is a 96 SS which is great :)

Answer 20

cross fingers :3

Answer 21

i still dont understand

Answer 22

anyway, @tpw1205 here's the deal :D
I'll expand the numerator, you expand the denominator, ok?
Here goes..
\[\Large \frac{\sin \left(x + \frac \pi 2\right)}{\cos \left(x + \frac \pi 2\right)}=\frac{\color{blue}{\sin(x)\cos\left(\frac \pi 2\right)+\cos(x)\sin\left(\frac \pi 2\right)}}{\cos\left(x+\frac \pi 2\right)}\]

Answer 23

ok

Answer 24

I used this identity:
\[\Large \sin(\alpha+\beta) = \sin(\alpha)\cos(\beta) +\cos(\alpha)\sin(\beta)\]

Use THIS identity with the denominator:
\[\Large \cos(\alpha+\beta) = \cos(\alpha)\cos(\beta) -\sin(\alpha)\sin(\beta)\]

Answer 25

Where \[\large \alpha = x\]\[\large \beta = \frac \pi 2\]

Answer 26

thanks