Analysis and Approaches for IBDP Maths Ebook 2 | Page 71

22
Paper 1 Section A – Compound Angle Formulae
Example
� and � are acute angles such that
sin(2 �� �)
.
1
sin� � and
4
3
cos � � . Find the value of
4
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Solution
2
cos�
� 1�
sin �
�1
�
cos�
� 1� � �
�4
�
cos� �
15
4
sin � �
2
1�
cos �
2
(A1) for substitution
7
�3
�
sin � � 1� � �
�4
�
2
7
sin � �
4
sin(2 � � �) � sin 2� cos � � cos 2� sin �
A1
2
sin(2 ) (2sin cos ) cos (2cos 1)sin
� � � � � � � � � � � A1
(A1) for substitution
2
1 15 3
�
15
�
� �� �� � � � � 7 �
sin(2 � � �) � 2� � � � � �2 �1�
� 4 �
� 4 �
� 4 � � � 4 � �� 4 �
(A1) for substitution
� � � � � �� �
6 15 �7 �� 7 �
sin(2 � � �)
� � � � 64 �8 �� 4 �
�� �
3 15 7 7
sin(2 � � �)
� �
32 32
3 15 � 7 7
sin(2 � ��)
� A1
32
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