big_bang344
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Can someone help me with question 10 exercise 21 (d) in the 3 unit fitzpatrick book?
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Fitzpatrick trig question (1 Viewer)
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SpiralFlex
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Question
If
, express each of the following in terms of 
.
Remember the formulae of tangent!
Times numerator and denominator by)
}{1-t^2+2t^2})
}{t^2+1})
If
Remember the
Times numerator and denominator by
if t=tan[theta/2],
tan[theta]=2t/(1-t^2)
cot[theta/2]=1/t
.'. you get {[2t/(1-t^2)] - t}/{1/t + [2t/(1-t^2)]}
= {[2t-t(1-t^2)]/(1-t^2)}/{[1-t^2+2t^2]/[t(1-t^2)]}
= {[2t-t+t^3]/(1-t^2)}/{[1+t^2]/[t(1-t^2)]}
= {[t(1+t^2]/(1-t^2)}/{[1+t^2]/t(1-t^2)]}
from this you can cancel some of the top and bottom parts out, and you end up with:
t/[1/t] = t^2
p.s. sorry, i dunno how to use latex
tan[theta]=2t/(1-t^2)
cot[theta/2]=1/t
.'. you get {[2t/(1-t^2)] - t}/{1/t + [2t/(1-t^2)]}
= {[2t-t(1-t^2)]/(1-t^2)}/{[1-t^2+2t^2]/[t(1-t^2)]}
= {[2t-t+t^3]/(1-t^2)}/{[1+t^2]/[t(1-t^2)]}
= {[t(1+t^2]/(1-t^2)}/{[1+t^2]/t(1-t^2)]}
from this you can cancel some of the top and bottom parts out, and you end up with:
t/[1/t] = t^2
p.s. sorry, i dunno how to use latex
big_bang344
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Oh god. I forgot to times the 2t by t. Anyways, thanks a lot guys!