Question

Verify the identity.please show all works.
Cot( theta - pai/2) = - tan theta.

Answer 1

Some identities:

cos(a-b) = cos(a)cos(b) + sin(a)sin(b)
sin(a-b) = sin(a)cos(b) - cos(a)sin(b)
cot(a) = 1/tan(a)

Therefore (substituting x for theta):

cos(x-pi/2) = cos(x)cos(pi/2) + sin(x)sin(pi/2)
----------------------
sin(x-pi/2) = sin(x)cos(pi/2) - cos(x)sin(pi/2)

cos(pi/2) =0
sin(pi/2) =1

So: sin(x)/-cos(x) = -tan(x)

Answer 2

Is this the way to do this?

Answer 3

Yes. You need to learn trig identities such as those jchick has typed here for you, and know when and how to apply them. More questions?

Answer 4

I don't understand how comcos( X- pi/2)=cos(X)cos(pi/2)+sin(X)sin(pi/2) is

Answer 5

@jchik please can you explain me more about

Answer 6

For any CO - trigonometric functions m(x) and co-m(x), this property is always true.
m(x)=co−m(π/2−x)=co−m(x−π/2).....or..vise..versa−−−−if..m(x)..is..even
m(x)=co−m(π/2−x)=−co−m(x−π/2).....or..vise..versa−−−−if..m(x)..is..odd

Answer 7

cot ( theta - pi / 2 )= cos ( theta - pi / 2 ) / sin ( theta - pi / 2 )

cos ( theta - pi / 2 )= cos(theta) cos (pi/2) + sin(theta) sin (pi/2)
= cos(theta) (0) + sin(theta) (1)
= sin(theta)

sin ( theta - pi / 2 )= sin(theta) cos(pi/2) - cos(theta) sin(pi/2)
= sin(theta) (0) - cos(theta) (1)
= -cos(theta)
so you get,
cot ( theta - pi / 2 )= sin(theta) / -cos(theta)
cot ( theta - pi / 2 )= -tan(theta)

Answer 8

Do you get it now?

Answer 9

Thank you so much

Answer 10

No problem!

Answer 11

@ Nnesha too long you tap on May you doing other way as well?

Answer 12

there is another to prove this identity by using Cofunctions Identities
where it says \[\large\rm \cot(\frac{\pi}{2}\color{Red}{-}\theta )=\tan x\]
first rewrite the left side as \[\cot[\color{red}{-}(\frac{\pi}{2}-\theta)]\]
i just take out the negative sign and then use the identity cot(pi/2-x)= tanx
and use the fact cot is an odd function
\[\large\rm \cot[\color{ReD}{-}(\frac{\pi}{2}-\theta)] \rightarrow \color{Red}{-} \cot(\frac{\pi}{2}-\theta)\]

Answer 13

~cot(-x)= -cot(x) ^^

Answer 14

Yes @Nnesha that would work as well.

Answer 15

I still need to work with using the equation tab. I am not used to having that function to teach with.

Answer 16

So, I confuse among this twos which is the most correct one?

Answer 17

Have you learned about the Confunctions?

Answer 18

Not yet

Answer 19

Ok then they probably aren't looking for it that way. So if you haven't learned about it put what I have as long as what I have is the way you have learned to do it.

Answer 20

Please show me I simple and understandable ways.

Answer 21

Do you understand what I have?

Answer 22

Of course I did

Answer 23

Ok then you have learned about it that way, only put what you know and if you know and understand what I have put that down.