Analysis and Approaches for IBDP Maths Ebook 2 | Page 129

(d)
2 � 4 � 6 �
0 � 1�15 tan �15 tan � tan
12 12 12
A1
6 � 4 � 2 �
tan �15 tan � 15 tan �1 � 0
12 12 12
AG
� 2 2 2 2
3cos � sin � ��
cos � 3sin
� �
� � �� � �
� 12 12 �� 12 12 �
4 � 2 � 2 � 4 �
� 3cos �10cos sin � 3sin
M1
12 12 12 12
5 � � 3 � 3 �
6 cos sin � 20 cos sin
12 12 12 12
� 5 �
�6cos
sin
� 12 12
� �
2sin cos
12 12
� � �
sin 6�
� 12
�
� �
A1A1
�
sin 6
1
�1� A1
2
[3]
� 2
AG
[4]
9
Exercise 39
1. (a) (i) Use the binomial theorem to expand
(cos�
isin )
4
� � .
(ii) Hence, express cos4� and sin 4� in terms of sin� and cos� .
Let z�r(cos�� isin �)
, where � is measured in radians, be the solution of
which has the smallest positive argument.
4
z � �
[6]
16i 0
(b) Find the values of r and � .
(c)
Hence, find the value of
3
cos 8
� , giving the answer in terms of surds.
[4]
(d)
Show that
3 3 3 3 3 3 1
sin � cos � �
cos � sin � ��
cos � sin
� �
� � �� � � � � .
8 8 � 8 8 �� 8 8 � 4
[6]
[3]
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