Analysis and Approaches for IBDP Maths Ebook 2 | Page 131

4. (a) Use De Moivre’s theorem to express sin� and cos� in terms of sin 5
� and
cos 5
� .
(b)
Hence, show that
� �
2� 4�
�
tan �5 �10 tan � tan �
5 5 5
tan�
�
�
�
2�
4�
1�10 tan �5tan
5 5
�
(c) Hence, use the substitution x � tan to solve the equation x
5
, where cos� � 0 .
�10x
�5 � 0 .
4 2
[6]
[3]
(d)
Hence, evaluate
[4]
(i)
4
r�
� tan , 5
r�0
(ii)
� 2� tan tan .
5 5
[7]
9
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