inverse trig (1 Viewer)

[jemsta]

how do i freakin prove that tan(pi-@) where x is a positive number and @=tan^-1 x?
the answer is cot x but im not sure if its the correct approach

 

[Trev]

What what?

 

[jemsta]

if you have the 3 unit year 12 cambridge book i think its question 14 a) where i have to simplify...not prove tan(pi/2-@) where you let x be a positive number and @=inverse tan x.
and then b)
show that inverse tan 1/x= pi/2 - inverse tan x
sorry about the error

 

[acmilan]

tan(pi/2 - @) = cot @ = cot(tan^-1x) = 1/tan(tan^-1x) = 1/x

Is that what you mean?

So if tan(pi/2 - @) = 1/x

inverse tan both sides, so tan^-1tan(pi/2 - @) = tan^-1(1/x)

Hence tan^-1(1/x) = pi/2 - @ = pi/2 - tan^-1x

 

[香港!]

if you have the 3 unit year 12 cambridge book i think its question 14 a) where i have to simplify...not prove tan(pi/2-@) where you let x be a positive number and @=inverse tan x.
and then b)
show that inverse tan 1/x= pi/2 - inverse tan x
sorry about the error

simplify tan(pi\2-@)=sin(pi\2-@)\cos(pi\2-@)
=(sin(pi\2)cos@-cos(pi\2)sin@)\(cos(pi\2)cos@+sin(pi\2)sin@)
=cos@\sin@=cot@

"show that inverse tan 1/x= pi/2 - inverse tan x"
tan (tan^-1 (1\x))=1\x
tan(pi\2-tan^-1x)=cot (tan^-1 x)
let tan^-1 x=@
tan@=x
so cot@=1\tan@=1\x
.: tan^-1 (x\1)=pi\2-tan^-1 x

 

[dave28]

hi, a bit off the topic, but on page A32 of math ext excel book, 7)1) talks about particle dispacement:
i) find a
x=1 + cos ^2 t
v = -4sin t cos t
a= -4 (cost cost - sint sint)
a= 4(sin^2 t - cos^2 t)

ive never seen this kind of question before (differentiation of cos ^2 t), so could someone please explain it? slightly worrying that im stuffed on a review of 2U work, but still...

 

[krabby_me]

Could u write the q out a bit clearer and ill try have a go

 

[MarsBarz]

Differentiation of cos²t


y =cos²t
y = (cos t)²
y' = 2(cos t) . (-sin t)
y' = -2sintcost

 

[krabby_me]

sorry i complete forgot about u.

cos ^2 t

we know Cos 2A = cos ^2 A - sin ^2 A, and that sin ^2 A + cos ^2 A = 1

so cos 2A = cos ^2 A - (1 - cos ^2 A)

= 2cos ^2 A - 1

cos 2A +1= 2cos ^2 A

.: cos ^2 A= 1/2(cos 2A +1)

.: cos ^2 T= 1/2cos 2T +1\2

use intergration table or common knowledge to differentiate 1/2cos 2T +1\2

 

[dave28]

thanks, i was looking for some complicated formula & forgot to just use the bracket differentiation (product rule?)