Quiz 2 Quiz 2                              Friday, March 16, 2001



NAME:

Student Number:------            No.----           Marks ----






(20 Marks) Show that cos(2tan-1x) = [(1-x2)/(1+x2)].

Solution. Let q = tan-1x. Then tanq = x and q (-p/2, p/2). This implies


cos(2tan-1x)
=
cos2q = 2cos2q-1
=
2
sec2q
-1
=
2
1+tan2q
-1
=
2-1-tan2q
1+tan2q
=
1-tan2q
1+tan2q
=
1-x2
1+x2
.



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On 3 Apr 2001, 11:21.