Show that tan ⁡ α + 5 sin ⁡ α 2 ( 5 cos ⁡ α − 1 ) is equivalent to 5 4 sin ⁡ ( 2 α ) − 1 2 tan ⁡ αI tried: sin ⁡ α cos ⁡ α + sin ⁡ α 2 ( 5 cos ⁡ α − 1 ) = sin ⁡ α + 5 sin ⁡ α cos ⁡ α cos ⁡ α 2 ( 5 cos ⁡ α − 1 ) = sin ⁡ α cos ⁡ α ( 5 cos ⁡ α + 1 ) 2 ( 5 cos ⁡ α − 1 ) = tan ⁡ α ( 5 cos 2 ⁡ α − 1 ) 2 = ? ? ?

Question

Show that             tan      ⁡      α      +              5            sin      ⁡      α        2    (      5    cos  ⁡  α  −  1  ) is equivalent to       5    4    sin  ⁡  (  2  α  )  −      1    2    tan  ⁡  αI tried:                              sin          ⁡          α                          cos          ⁡          α                    +      sin      ⁡      α        2    (      5    cos  ⁡  α  −  1  )  =                      sin        ⁡        α        +                  5                sin        ⁡        α        cos        ⁡        α                    cos        ⁡        α              2    (      5    cos  ⁡  α  −  1  )  =                                sin          ⁡          α                          cos          ⁡          α                    (              5            cos      ⁡      α      +      1      )        2    (      5    cos  ⁡  α  −  1  )  =              tan      ⁡      α      (      5              cos        2            ⁡      α      −      1      )        2    =    ?  ?  ?

odmeravan5c · Accepted Answer

Now simply            5      sin      ⁡      α      cos      ⁡      α      −      tan      ⁡      α        2              5      ×      2.      sin      ⁡      α      cos      ⁡      α        4    −            tan      ⁡      α        2                      (sin2x=2 sinx cox)                                          5            ×            sin            ⁡            2            α                    4                −                              tan            ⁡            α                    2

Show that tan ⁡ α + <msqrt>

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