Solve for x: 2 sin 2 ⁡ ( x ) − sin 2 ⁡ ( 2 x ) = cos 2 ⁡ ( 2 x )

Question

Solve for x:   2      sin    2    ⁡  (  x  )  −      sin    2    ⁡  (  2  x  )  =      cos    2    ⁡  (  2  x  )

ontzeidena8a · Accepted Answer

Your equation is simply  2      sin    2    ⁡  (  x  )  =                                          cos            2                    ⁡          (          2          x          )          +                      sin            2                    ⁡          (          2          x          )                ⏟                    =      1      Whence      sin    2    ⁡  (  x  )  =      1    2  Can you proceed from here?Solution  sin  ⁡  (  x  )  =  ±            2        2  This is a well known value and it&#039;s   π      /    4 radians and   3  π      /    4 radians. Since we have       sin    2  , to be then explicit in the solution we have also   −  π      /    4 and   5  π      /    4 radians:  x  =  ±      π    4    +  2  k  π                                   k  ∈      Z    x  =            3      π        4    +  2  k  π                                   k  ∈      Z    x  =            5      π        4    +  2  k  π                                   k  ∈      Z

Solve for x: 2 sin^2(x)−sin^2 (2x)=cos^2 (2x)

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