Let  .

1. State all possible values of .   (1 mark)
   

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2. Hence, find all possible solutions for , where    (2 marks)
   

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Solve the equation    for  .   (2 marks)

Find all solutions of the equation  ,  for     (3 marks)

Solve     (2 marks)

Express    as a single fraction in terms of , given all angles are measured in degrees.   (3 marks)

Determine the number of values of in the range    that satisfy the equation