(1 + tan ^x) (1-cos^x) =

[tex] 1 + tan^2x = sec^2 x [/tex]
[tex] 1 - cos^2x = sin^2 x [/tex]

Maka,
[tex] = sec^2. sin^2x [/tex]
[tex] = \frac{1} {cos^2x}.sin^2x [/tex]
[tex] = tan^2 x [/tex]