| Date | May 2017 | Marks available | 5 | Reference code | 17M.1.hl.TZ1.3 |
| Level | HL only | Paper | 1 | Time zone | TZ1 |
| Command term | Solve | Question number | 3 | Adapted from | N/A |
Question
Solve the equation \({\sec ^2}x + 2\tan x = 0,{\text{ }}0 \leqslant x \leqslant 2\pi \).
Markscheme
METHOD 1
use of \({\sec ^2}x = {\tan ^2}x + 1\) M1
\({\tan ^2}x + 2\tan x + 1 = 0\)
\({(\tan x + 1)^2} = 0\) (M1)
\(\tan x = - 1\) A1
\(x = \frac{{3\pi }}{4},{\text{ }}\frac{{7\pi }}{4}\) A1A1
METHOD 2
\(\frac{1}{{{{\cos }^2}x}} + \frac{{2\sin x}}{{\cos x}} = 0\) M1
\(1 + 2\sin x\cos x = 0\)
\(\sin 2x = - 1\) M1A1
\(2x = \frac{{3\pi }}{2},{\text{ }}\frac{{7\pi }}{2}\)
\(x = \frac{{3\pi }}{4},{\text{ }}\frac{{7\pi }}{4}\) A1A1
Note: Award A1A0 if extra solutions given or if solutions given in degrees (or both).
[5 marks]
Examiners report
[N/A]
