While doing a sum I was stuck in a particular step: r 1 = 4 a cos ⁡ θ sin 2 ⁡ θ and r 2 = 4 a sin ⁡ θ cos 2 ⁡ θ How to eliminate θ?

Question

While doing a sum I was stuck in a particular step:      r    1    =            4      a      cos      ⁡      θ                      sin        2            ⁡      θ      and      r    2    =            4      a      sin      ⁡      θ                      cos        2            ⁡      θ      How to eliminate   θ?

enfeinadag0 · Accepted Answer

r    1    ⋅      r    2    =            (      4      a              )        2                    sin      ⁡      θ      cos      ⁡      θ                  (                        r          2                          r          1                    )                      1        3              =            sin      ⁡      θ              cos      ⁡      θ                          (                              r            2                                r            1                          )                              1          3                                    r        1            ⋅              r        2              =                    sin        2            ⁡      θ              (      4      a              )        2              =      r    1          −              4        3                  r    1          −              2        3                  1                            (                                    r              2                                      r              1                                )                                      1            3                                      r        1            ⋅              r        2              =                    cos        2            ⁡      θ              (      4      a              )        2              =      r    1          −              2        3                  r    1          −              4        3              ∴      r    1          −              4        3                  r    2          −              2        3              +      r    1          −              2        3                  r    2          −              4        3              =      1          (      4      a              )        2

While doing a sum I was stuck in a particular step: r 1 </msub> =

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