Student Number:_{------}
No._{----} Marks _{----}

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

cos(2tan ^{-1}x)
=
cos2q = 2cos ^{2}q-1
=
2

sec^{2}q
-1
=
2

1+tan^{2}q
-1
=
2-1-tan ^{2}q

1+tan^{2}q
=
1-tan ^{2}q

1+tan^{2}q
=
1-x ^{2}

1+x^{2}
.

File translated from T

On 3 Apr 2001, 11:21.