Trigonometric equation, find sin ⁡ θFind sin ⁡ θ if a and c are constants 1 − ( c − a tan ⁡ θ ) 2 = sin 2 ⁡ θ cos 4 ⁡ θ a 2 − cos 4 ⁡ θ

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Trigonometric equation, find   sin  ⁡  θFind   sin  ⁡  θ if   a and   c are constants  1  −            (      c      −      a      tan      ⁡      θ      )        2    =                    sin        2            ⁡      θ              cos        4            ⁡      θ                      a        2            −              cos        4            ⁡      θ

inmholtau5 · Accepted Answer

I think this relust is ugly.let  t  =  sin  ⁡      x    1  −            (      c      −      a      ⋅                        t                      ±                          1              −                              t                2                                                        )        2    =                              t          2                (        1        −                  t          2                          )          2                                      a          2                −        (        1        −                  t          2                          )          2                    so  (  1  −      t    2    )  −  (  ±  c      1    −          t      2        −  a  t      )    2    =                              t          2                (        1        −                  t          2                          )          3                                      a          2                −        (        1        −                  t          2                          )          2                    then  [      a    2    −  (  1  −      t    2        )    2    ]  [  (  1  −      t    2    )  −  (      c    2    (  1  −      t    2    )  −  ±  2  a  c  t      1    −          t      2        ]  =      t    2    (  1  −      t    2        )    3

Aldo Ashley · Accepted Answer

after simpßlification we find this here  2    sin  ⁡      (    θ    )              (      cos      ⁡              (        θ        )            )              5        a  c  −            (      cos      ⁡              (        θ        )            )              8        +            a              2                  (      cos      ⁡              (        θ        )            )              6        −            (      cos      ⁡              (        θ        )            )              6                  c              2        +  2              (      cos      ⁡              (        θ        )            )              6        −            (      cos      ⁡              (        θ        )            )              4                  a              2        −  2    sin  ⁡      (    θ    )              a              2        c  cos  ⁡      (    θ    )    −            a              3                  (      cos      ⁡              (        θ        )            )              2        +  a            c              2                  (      cos      ⁡              (        θ        )            )              2        −  a            (      cos      ⁡              (        θ        )            )              2        +            a              3        =  0i think it is implossible to find an explicit formula for   θ try a numerical method

Trigonometric equation, find sin theta Find sin theta if a and c are constants 1-(c-a tan theta)^2=(sin^2 theta cos^4 theta )/(a^2- cos^4 theta )

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