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Date May 2017 Marks available 5 Reference code 17M.1.AHL.TZ1.H_3
Level Additional Higher Level Paper Paper 1 (without calculator) Time zone Time zone 1
Command term Solve Question number H_3 Adapted from N/A

Question

Solve the equation sec 2 x + 2 tan x = 0 ,   0 x 2 π .

Markscheme

* 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 = 3 π 4 ,   7 π 4     A1A1

METHOD 2

1 cos 2 x + 2 sin x cos x = 0     M1

1 + 2 sin x cos x = 0

sin 2 x = 1     M1A1

2 x = 3 π 2 ,   7 π 2

x = 3 π 4 ,   7 π 4     A1A1

 

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

 

[5 marks]

Examiners report

[N/A]

Syllabus sections

Topic 3— Geometry and trigonometry » AHL 3.9—Reciprocal trig ratios and their pythagorean identities. Inverse circular functions
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Topic 3— Geometry and trigonometry

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