Trigonometry- Double Angle Trigonometric Equations tan ⁡ ( 3 x ) = ( ( tan ⁡ x ( 3 − tan 2 ⁡ x ) ) / ( 1 − 3 tan 2 ⁡ x ) )I'm just having a hard time seeing where the double angle formula fits in with verifying this equation.

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Trigonometry- Double Angle Trigonometric Equations  tan  ⁡  (  3  x  )  =  (  (  tan  ⁡  x  (  3  −      tan    2    ⁡  x  )  )      /    (  1  −  3      tan    2    ⁡  x  )  )I&#039;m just having a hard time seeing where the double angle formula fits in with verifying this equation.

Milton Gilmore · Accepted Answer

Using a Adicional formula:  tan  ⁡  (  x  +  y  )  =            tan      ⁡      x      +      tan      ⁡      y              1      −      tan      ⁡      x      tan      ⁡      y        ,we have:  tan  ⁡  (  2  x  +  x  )  =            tan      ⁡      2      x      +      tan      ⁡      x              1      −      tan      ⁡      2      x      tan      ⁡      x        =            tan      ⁡      (      x      +      x      )      +      tan      ⁡      x              1      −      tan      ⁡      (      x      +      x      )      tan      ⁡      x        =                              tan          ⁡          x          +          tan          ⁡          x                          1          −          tan          ⁡          x          tan          ⁡          x                    +      tan      ⁡      x              1      −                        tan          ⁡          x          +          tan          ⁡          x                          1          −          tan          ⁡          x          tan          ⁡          x                    tan      ⁡      x        =            tan      ⁡      x      +                        2          tan          ⁡          x                          1          −                      tan            2                    ⁡          x                            1      −      tan      ⁡      x                        2          tan          ⁡          x                          1          −                      tan            2                    ⁡          x                      =                    tan        ⁡        x        −                  tan          3                ⁡        x        +        2        tan        ⁡        x                    1        −                  tan          2                ⁡        x                            1        −                  tan          2                ⁡        x        −        2                  tan          2                ⁡        x                    1        −                  tan          2                ⁡        x              =            tan      ⁡      x      −              tan        3            ⁡      x      +      2      tan      ⁡      x              1      −              tan        2            ⁡      x      −      2              tan        2            ⁡      x        =            3      tan      ⁡      x      −              tan        3            ⁡      x              1      −      3              tan        2            ⁡      x        =            tan      ⁡      x      (      3      −              tan        2            ⁡      x      )              1      −      3              tan        2            ⁡      x

paratusojitos0yx · Accepted Answer

tan  ⁡  (  3  x  )  =            sin      ⁡      (      2      x      +      x      )              cos      ⁡      (      2      x      +      x      )        =            sin      ⁡      (      2      x      )      cos      ⁡      x      +      sin      ⁡      x      cos      ⁡      (      2      x      )              cos      ⁡      (      2      x      )      cos      ⁡      x      −      sin      ⁡      (      2      x      )      sin      ⁡      x        =            3      sin      ⁡      x      −      4              sin        3            ⁡      x              −      3      cos      ⁡      x      +      4              cos        3            ⁡      x        =  (  tan  ⁡  x  )            3      −      4              sin        2            ⁡      x              −      3      +      4              cos        2            ⁡      x

Trigonometry- Double Angle Trigonometric Equations tan(3x)=((tan x(3-tan^2x))/(1-3 tan^2x)) I'm just having a hard time seeing where the double angle formula fits in with verifying this equation.

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