Trigonometric equations tan ⁡ θ − sec ⁡ θ = 3

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Trigonometric equations   tan  ⁡  θ  −  sec  ⁡  θ  =      3

zwichtsu · Accepted Answer

tan  ⁡      θ    −    sec    ⁡          θ        =          3                    sin      ⁡              θ                    cos      ⁡              θ              −      1          cos      ⁡              θ              =      3      sin  ⁡      θ    −          3        cos    ⁡          θ      =      1        divide both side to 2      1    2    sin  ⁡      θ    −                  3            2        cos  ⁡      θ    =      1    2      sin  ⁡            π      6        sin    ⁡          θ        −    cos    ⁡                  π        6            cos      ⁡              θ        =                  1                      2                                              cos  ⁡            (              π        6            +      θ      )        =    −          1      2              π    6    +  θ  =  ±  arccos  ⁡            (      −              1        2            )        +    2    n    π    =    ±          (      π      −              π        3            )        +  2  n  π    θ  =  ±            2      π        3    −      π    6    +  2  n  π  ,  n  ∈      Z

Trigonometric equations tan ⁡

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