How would I solve the following trigonometric equation? 2 cot ⁡ 2 x cos ⁡ 2 x = 1 − sin ⁡ 2 xI got to this stage: 2 cos 2 ⁡ 2 x = sin ⁡ 2 x − sin 2 ⁡ 2 xHow do I continue?

Question

How would I solve the following trigonometric equation?  2  cot  ⁡  2  x  cos  ⁡  2  x  =  1  −  sin  ⁡  2  xI got to this stage:   2      cos    2    ⁡  2  x  =  sin  ⁡  2  x  −      sin    2    ⁡  2  xHow do I continue?

pressacvt · Accepted Answer

2  c  o  t  2  x  c  o  s  2  x  =  1  −  s  i  n  2  x                      cos                  2                    ⁡              2        x                    sin      ⁡              2        x              =            1      −      sin      ⁡              2        x              2      2      (    1    −          sin              2              ⁡          2      x        )    +      sin          2        ⁡      2    x    −  sin  ⁡      2    x    =  0        sin          2        ⁡      2    x    +  sin  ⁡      2    x    −  2  =  0    sin  ⁡      2    x    =            −      1      ±      3        2      sin  ⁡      2    x    ≠    −    2    ,  sin  ⁡      2    x    =  1    sin  ⁡      2    x    =  1  ⇒  2  x  =      π    2    +  2  n  π  ⇒  so the final answer is:  x  =      π    4    +  n  π

How would I solve the following trigonometric equation? 2 cot ⁡ 2

Answered question

Answer & Explanation

New Questions in Trigonometry