Fitzpatrick trig question (1 Viewer)

big_bang344 · Dec 1, 2011

Can someone help me with question 10 exercise 21 (d) in the 3 unit fitzpatrick book?

SpiralFlex · Dec 1, 2011

Question

If $\tan \frac{\theta}{2}=t$ , express each of the following in terms of $t$ .

$\frac{\tan \theta-\tan \frac{\theta}{2}}{cot \frac{\theta}{2}+\tan \theta}$

Remember the $t$ formulae of tangent!

$\tan \theta = \frac{2t}{1-t^2}$

$\frac{\frac{2t}{1-t^2}-t}{\frac{1}{t}+\frac{2t}{1-t^2}}$

Times numerator and denominator by $t(1-t^2)$

$\frac{2t^2-t^2(1-t^2)}{1-t^2+2t^2}$

$=\frac{t^4+t^2}{t^2+1}$

$=\frac{t^2(t^2+1)}{t^2+1}$

$=t^2$

Aesytic · Dec 1, 2011

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

big_bang344 · Dec 1, 2011

Oh god. I forgot to times the 2t by t. Anyways, thanks a lot guys!

Fitzpatrick trig question (1 Viewer)

big_bang344

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SpiralFlex

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Aesytic

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big_bang344

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