Hi, please help. I ain't no scam, Real 50 point question. Find all solutions in the interval [0, 2π).

x ∈ { π/4 , 3 π/ 4 , 5 π /4 , 7 π /4 } Explanation: Applying the identity cos^ 2 ( x ) − sin^ 2 ( x ) = cos ( 2 x ) we have sin^ 2 ( x ) − cos^ 2 ( x ) = − cos ( 2 x ) In general, cos ( u ) = 0 ⇔ u = n π /2 for some n ∈ Z Thus we have sin ^2 ( x ) − cos ^2 ( x ) = 0 ⇒ − cos ( 2 x ) = 0 ⇒ 2 x = n π /2 for n ∈ Z ⇒ x = n π /4 for n ∈ Z Restricting our values to the interval [ 0 , 2 π ] gives our final result: x ∈ { π /4 , 3 π /4 , 5 π /4 , 7 π/ 4 }