18M.2.AHL.TZ1.H_3

pestleMathematicsAAHLPaper 218M· ahl-3-10-compound-angle-identitiessource ↗

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 $x$ .

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

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