Analysis and Approaches for IBDP Maths Ebook 1 | Page 105

Front Page
36
Paper 1 Section A – Trigonometric
identities and rules of logarithm
Example
(a)
�
Show that � cos 2 x� log
4 � cos 2 x
25 � � � log5
.
� 2 �
2
(b)
�4 � cos 2x
�
Solve log5 2cos x � log25
� �
� 2 � for 0 �
� x � .
2
[3]
[5]
Solution
�4 � cos 2x
�
(a) log
25 � �
� 2 �
�4 � cos 2x
�
log5
� �
2
�
� �
M1A1
log 25
5
1 � 4 � cos 2x
�
2 � 2 �
� log5
� �
1
�4 � cos 2x
�2
� log5
� �
�
2
�
4 � cos 2x
� log5
AG N0
2
�4 � cos 2x
�
log 2cos x � log � �
� 2 �
(b) 5 25
log 2cos x � log
5 5
4 � cos 2x
2
A1
2cos x �
4 � cos 2x
2
M1
2 4 � cos 2x
4cos x �
2
A1
2 2
8cos x� 4� 2cos x� 1
M1
2
6cos x � 3
cos
x �
2
2 1
[3]
10
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