12 . ( a ) Use De Moivre ’ s theorem to express sin� and cos� in terms of sin 7
�
� and cos . 7
[ 6 ]
( b ) Hence , by considering the expression of tan� and use a suitable substitution , show that the equation roots .
( c ) Hence , evaluate
6 4 2 x � 21x �35x
�7 � 0 has six real
[ 7 ]
( i )
7 r�
� tan , 7 r�1
( ii )
� 2� 3� tan tan tan . 7 7 7
[ 7 ]
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