(a) (i) Given that tan 2x+tan x = 0, show that tan.x = 0 or tan²x = 3. (ii) Hence find all solutions of tan 2x+tan.x = 0 in the interval 0°

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.4: Multiple-angle Formulas
Problem 50E
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(a) (i) Given that tan 2x tanx = 0, show that tan.x = 0 or tan²x = 3.
(ii)
Hence find all solutions of tan 2x tan x
+
(b) (i) Given that cos.x 0, show that the equation
sin 2x cos x cos 2x
can be written in the form
0 in the interval 0° <x< 180°.
2 sin²x2 sinx-1=0
(ii) Show that all solutions of the equation 2 sin²x+2 sinx1=0 are given by
√3-1
sin .x
P
-, where p is an integer.
Transcribed Image Text:(a) (i) Given that tan 2x tanx = 0, show that tan.x = 0 or tan²x = 3. (ii) Hence find all solutions of tan 2x tan x + (b) (i) Given that cos.x 0, show that the equation sin 2x cos x cos 2x can be written in the form 0 in the interval 0° <x< 180°. 2 sin²x2 sinx-1=0 (ii) Show that all solutions of the equation 2 sin²x+2 sinx1=0 are given by √3-1 sin .x P -, where p is an integer.
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