Arihangdu
  • Arihangdu
Verify the identity.please show all works. Cot( theta - pai/2) = - tan theta.
Algebra
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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jchick
  • jchick
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)
Arihangdu
  • Arihangdu
Is this the way to do this?
mathmale
  • mathmale
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?

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Arihangdu
  • Arihangdu
I don't understand how comcos( X- pi/2)=cos(X)cos(pi/2)+sin(X)sin(pi/2) is
Arihangdu
  • Arihangdu
@jchik please can you explain me more about
jchick
  • jchick
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
jchick
  • jchick
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)
jchick
  • jchick
Do you get it now?
Arihangdu
  • Arihangdu
Thank you so much
jchick
  • jchick
No problem!
Arihangdu
  • Arihangdu
@ Nnesha too long you tap on May you doing other way as well?
Nnesha
  • Nnesha
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 \[\large\rm \cot[\color{ReD}{-}(\frac{\pi}{2}-\theta)] \rightarrow \color{Red}{-} \cot(\frac{\pi}{2}-\theta)\]
Nnesha
  • Nnesha
~cot(-x)= -cot(x) ^^
jchick
  • jchick
Yes @Nnesha that would work as well.
jchick
  • jchick
I still need to work with using the equation tab. I am not used to having that function to teach with.
Arihangdu
  • Arihangdu
So, I confuse among this twos which is the most correct one?
jchick
  • jchick
Have you learned about the Confunctions?
Arihangdu
  • Arihangdu
Not yet
jchick
  • jchick
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.
Arihangdu
  • Arihangdu
Please show me I simple and understandable ways.
jchick
  • jchick
Do you understand what I have?
Arihangdu
  • Arihangdu
Of course I did
jchick
  • jchick
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.

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