Solving 11 ⋅ sin ⁡ ( x ) 2 − 2 sin ⁡ ( x ) 2 + 5 ⋅ cot ⁡ ( x ) = 3 − cot ⁡ ( x )

Question

Solving                     11        ⋅        sin        ⁡        (        x                  )          2                −        2                    sin        ⁡        (        x                  )          2                      +    5    ⋅    cot    ⁡    (    x    )    =  3  −  cot  ⁡  (  x  )

Laura Fletcher · Accepted Answer

11              ⋅                              sin                2                            ⁡              (              x              )              −              2                                                      sin                2                            ⁡              (              x              )                                +          5          ⋅          cot          ⁡          x                =        3        −        cot        ⁡        x            Square both sides,                              11                      sin            2                    ⁡          (          x          )          −          2                +        2.5        sin        ⁡        2        x        =        8                  sin          2                ⁡        x        +        1        −        3        sin        ⁡        2        x                                ⇒        3                  sin          2                ⁡        (        x        )        −        3        +        5.5        sin        ⁡        2        x        =        0                                ⇒        1.5        (        1        −        cos        ⁡        2        (        x        )        )        −        3        +        5.5        sin        ⁡        2        x        =        0                                ⇒        11        sin        ⁡        2        x        −        3        cos        ⁡        2        x        −        3        =        0

Adison Rogers · Accepted Answer

Hint            11      sin      ⁡      (      x              )        2            −      2              sin      ⁡      (      x              )        2              =            11      sin      ⁡      (      x              )        2            −      2      sin      ⁡      (      x              )        2            −      2      cos      ⁡      (      x              )        2                    sin      ⁡      (      x              )        2              =  9  −  2  cot  ⁡  (  x      )    2  Make   t  =  cot  ⁡  (  x  ), square, solve for t and check if squaring did or not introduce extra solutions

Solving sqrt((11 * sin(x)^2−2)/(sin(x)^2)+5 * cot(x))=3-cot(x)

Answered question

Answer & Explanation

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