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Question
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 \(x\).
Answer/Explanation
Markscheme
\({\text{tan}}\left( {x + \pi } \right) = \tan x\left( { = \frac{{{\text{sin}}\,x}}{{{\text{cos}}\,x}}} \right)\) (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]
Examiners report
[N/A]