17M.1.AHL.TZ1.H_3

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

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

$x=\frac{3\pi }{4},\frac{7\pi }{4}$     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

$2x=\frac{3\pi }{2},\frac{7\pi }{2}$

$x=\frac{3\pi }{4},\frac{7\pi }{4}$     A1A1

 

Note:     Award A1A0 if extra solutions given or if solutions given in degrees (or both).

 

[5 marks]

[N/A]