Analysis and Approaches for IBDP Maths Ebook 2 | Page 70

Your Practice Set – Analysis and Approaches for IBDP Mathematics
21
Paper 1 Section A – Trigonometric Equations
Example
Solve the equation
� � , 0�x
� 2�
.
2
tan x sec x 1
[5]
Solution
2
tan x�sec x�
1
2
sec x 1 sec x 1
� � � (A1) for substitution
2
sec x�sec x� 2 � 0
(sec x�1)(sec x� 2) � 0
(A1) for factorization
sec x �� 1 or sec x � 2
1
cos x �� 1 or cos x � A1
2
� �
x � � or x � , x �2�
�
3 3
�
5�
�x
� , x � � or x � A2
3
3
[5]
Exercise 21
1. Solve the equation tan 2x� tan x, 0�x
� 4�
.
[5]
2. Solve the equation
3. Solve the equation
� � , 0 �x � � .
2
cosec x 2cot x 0
�
� � , � x � � . 2
2
sec 2x
tan 2x
1
[4]
[5]
4. Solve the equation tan x�cot x� 4, 0 �x � � .
[5]
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