SOLUTION: Can someone please help me solve these two problems for THETA θ sin^4 2θ - 2 sin^2 2θ = -1 (3tan 3θ)^2 - 27 = 0

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Question 1122857: Can someone please help me solve these two problems for THETA θ
sin^4 2θ - 2 sin^2 2θ = -1
(3tan 3θ)^2 - 27 = 0

Answer by ikleyn(52795)   (Show Source): You can put this solution on YOUR website!
.
 -  = -1  <====>  (is equivalent to) 


 = 0  <====>  (is equivalent to)


 = 0  <====>  (is equivalent to)


 = 0  <====>  (is equivalent to) 


 = 1   <====>  (is equivalent to)


 = +/- 1.


    Case 1.   = 1   is equivalent to   = , , , . . . , ,  where n is any integer.

             General solution for this case is   = ,  where n is any integer.



    Case 2.   = -1   is equivalent to   = , , , . . . , ,  where n is any integer.

             General solution for this case is   = ,  where n is any integer



Answer.  Any angle of the set  ,   is the solution, where k is any integer.

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