Let $f\left( x \right) = {\text{tan}}\left( {x + \pi } \right){\text{cos}}\left( {x - \frac{\pi }{2}} \right)$ where $0 < x < \frac{\pi }{2}$.

Express $f\left( x \right)$ in terms of sin $x$ and cos $x$.

${\text{tan}}\left( {x + \pi } \right) = \tan x\left( { = \frac{{{\text{sin}}\,x}}{{{\text{cos}}\,x}}} \right)$     (M1)A1

${\text{cos}}\left( {x - \frac{\pi }{2}} \right) = {\text{sin}}\,x$     (M1)A1

Note: The two M1s can be awarded for observation or for expanding.

${\text{tan}}\left( {x + \pi } \right) = {\text{cos}}\left( {x - \frac{\pi }{2}} \right) = \frac{{{\text{si}}{{\text{n}}^2}\,x}}{{{\text{cos}}\,x}}$     A1

[5 marks]