Proving the identity cos 2 ⁡ θ + tan 2 ⁡ θ − 1 sin 2 ⁡ θ = tan 2 ⁡ θ

Question

Proving the identity                     cos        2            ⁡      θ      +              tan        2            ⁡      θ      −      1                      sin        2            ⁡      θ        =      tan    2    ⁡  θ

Selena Pratt · Accepted Answer

cos        2            ⁡      θ      +                                    sin            2                    ⁡          θ                                      cos            2                    ⁡          θ                    −      1                      sin        2            ⁡      θ        =  =                    cos        2            ⁡      θ      +                                    sin            2                    ⁡          θ                                      cos            2                    ⁡          θ                    −              sin        2            ⁡      θ      −              cos        2            ⁡      θ                      sin        2            ⁡      θ        =                              sin          2                ⁡        θ        −                  cos          2                ⁡        θ        ⋅                  sin          2                ⁡        θ                              cos          2                ⁡        θ                            sin        2            ⁡      θ        =                    sin        2            ⁡      θ      ⋅      (      1      −              cos        2            ⁡      θ      )                      sin        2            ⁡      θ      ⋅              cos        2            ⁡      θ        =                    sin        2            ⁡      θ      ⋅              sin        2            ⁡      θ              s      i              n        2            θ      ⋅              cos        2            ⁡      θ        =                    sin        2            ⁡      θ                      cos        2            ⁡      θ        =      tan    2    ⁡  θ

Proving the identity cos 2 </msup> ⁡<!-- ⁡

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