How to find x in some trigonometric equationsHow to solve these trigonometric equations? tan ⁡ 2 x − sin ⁡ 4 x = 0and tan ⁡ 2 x = sin ⁡ xI can't do this, please help me! I did this: tan ⁡ 2 x = 2 sin ⁡ x sin ⁡ 2 x cos ⁡ 2 x = tan ⁡ x

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How to find x in some trigonometric equationsHow to solve these trigonometric equations?  tan  ⁡  2  x  −  sin  ⁡  4  x  =  0and  tan  ⁡  2  x  =  sin  ⁡  xI can&#039;t do this, please help me! I did this:                    tan        ⁡        2        x                            =        2        sin        ⁡        x                                                                sin            ⁡            2            x                                cos            ⁡            2            x                                              =        tan        ⁡        x

Nigerkamg5 · Accepted Answer

sin  ⁡      2    x    =                                                  2          tan          ⁡          x                                                                  1          +                      tan            2                    ⁡          x                    Just to be clear on how to use this substitution:  tan  ⁡      2    x    =  sin  ⁡      4    x    =                                                  2          tan          ⁡          2          x                                                                  1          +                      tan            2                    ⁡          2          x                    Then we have   tan  ⁡      2    x    =  0 or   1  +      tan    2    ⁡      2    x    =  2 and in this case   tan  ⁡      2    x    =  ±  1... from which point we are reduced to considering simple cases.

reevelingw97 · Accepted Answer

Usually, equations with trigonometric functions in them can be solved by substitution using identities. If you know your trigonometric identities really well, then solving these types of equations becomes less difficult. For the first equation, you have  tan  ⁡  2  x  =  sin  ⁡  4  xIn this case, you can use the fact that   tan  ⁡  x  =                                                  sin          ⁡          x                                                                  cos          ⁡          x                     to substitute for   tan  ⁡  2  x. Also, there&#039;s another identity which states that   sin  ⁡  2  x  =  2  sin  ⁡  x  cos  ⁡  x, so you can substitute using this identity for   sin  ⁡  4  x. This will give you                                                  sin          ⁡          2          x                                                                  cos          ⁡          2          x                      =  2  sin  ⁡  2  x  cos  ⁡  2  xYou should then be able to solve this equation by multiplying through by   cos  ⁡  2  x and using the identity       cos    2    ⁡      x    =  1  −      sin    2    ⁡      x  Using the identity   tan  ⁡  x  =                                                  sin          ⁡          x                                                                  cos          ⁡          x                     and the fact that       cos    2    ⁡  x  =  1  −      sin    2    ⁡  x, you can manipulate the above to produce                                                  2                                                                                                                  sin                  ⁡                  x                                                                                                                                                  cos                  ⁡                  x                                                                                                                      1          −                                                                                                                                      sin                    2                                    ⁡                  x                                                                                                                                                  1                  −                                      sin                    2                                    ⁡                  x                                                                          =  sin  ⁡  xThis simplifies to  sin  ⁡                                                                    x                                                                                      2                                (  2      cos    2    ⁡  x  −  2  cos  ⁡  x  −  1  )  =  0Then you just have to check to make sure that solutions to the above equation are well-defined in the original equation.

How to find x in some trigonometric equations How to solve these trigonometric equations? tan2x−sin4x=0 and tan2x=sinx I can't do this, please help me! I did this: tan2x=2sinx (sin2x)/(cos2x)=tan x

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