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]