Solving $sectheta - 1 = left(sqrt2 - 1right) tantheta$

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Solve
$$sectheta - 1 = left(sqrt2 - 1right) tantheta$$




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Is there any process possible for this equation? Please share it.




trigonometry




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    Your solution is correct. Please read this tutorial on how to typeset mathematics on this site.
    – N. F. Taussig
    Aug 17 at 10:10














up vote
-1
down vote

favorite













Solve
$$sectheta - 1 = left(sqrt2 - 1right) tantheta$$




My try :enter image description here



Is there any process possible for this equation? Please share it.




trigonometry




share|cite|improve this question


















  • 1




    Your solution is correct. Please read this tutorial on how to typeset mathematics on this site.
    – N. F. Taussig
    Aug 17 at 10:10












up vote
-1
down vote

favorite









up vote
-1
down vote

favorite












Solve
$$sectheta - 1 = left(sqrt2 - 1right) tantheta$$




My try :enter image description here



Is there any process possible for this equation? Please share it.




trigonometry




share|cite|improve this question















Solve
$$sectheta - 1 = left(sqrt2 - 1right) tantheta$$




My try :enter image description here



Is there any process possible for this equation? Please share it.





trigonometry





share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 17 at 5:31









Blue

43.8k868141




43.8k868141










asked Aug 17 at 5:17









user580093

6015




6015







  • 1




    Your solution is correct. Please read this tutorial on how to typeset mathematics on this site.
    – N. F. Taussig
    Aug 17 at 10:10












  • 1




    Your solution is correct. Please read this tutorial on how to typeset mathematics on this site.
    – N. F. Taussig
    Aug 17 at 10:10







1




1




Your solution is correct. Please read this tutorial on how to typeset mathematics on this site.
– N. F. Taussig
Aug 17 at 10:10




Your solution is correct. Please read this tutorial on how to typeset mathematics on this site.
– N. F. Taussig
Aug 17 at 10:10










2 Answers
2






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up vote
1
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accepted










Hint:



$$dfracsec2y-1tan2y=dfrac1-cos2ysin2y=tan y$$



Alternatively, $$sqrt2-1=dfracsec2y-1tan2y=csc2y-cot2y$$



$$iffcsc2y+cot2y=dfrac1csc2y-cot2y=?$$






share|cite|improve this answer



























    up vote
    2
    down vote













    HINT:



    Dividing tan theta both side you get - $$frac1-cosxsinx= sqrt2-1$$ Now square it on both sides , and solving further you will reach the solution.



    Additional hints: $$frac1-cosx1+cosx= 3-2sqrt2$$ $$cosx = frac1sqrt2 $$ and you are done.






    share|cite|improve this answer




















    • Are the answers of yours the same of main equation?
      – Nosrati
      Aug 17 at 5:41







    • 3




      two points: 1) division by tan theta deprived of one root; 2) squaring introduced extra root.
      – farruhota
      Aug 17 at 5:58










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    2 Answers
    2






    active

    oldest

    votes








    2 Answers
    2






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    1
    down vote



    accepted










    Hint:



    $$dfracsec2y-1tan2y=dfrac1-cos2ysin2y=tan y$$



    Alternatively, $$sqrt2-1=dfracsec2y-1tan2y=csc2y-cot2y$$



    $$iffcsc2y+cot2y=dfrac1csc2y-cot2y=?$$






    share|cite|improve this answer
























      up vote
      1
      down vote



      accepted










      Hint:



      $$dfracsec2y-1tan2y=dfrac1-cos2ysin2y=tan y$$



      Alternatively, $$sqrt2-1=dfracsec2y-1tan2y=csc2y-cot2y$$



      $$iffcsc2y+cot2y=dfrac1csc2y-cot2y=?$$






      share|cite|improve this answer






















        up vote
        1
        down vote



        accepted







        up vote
        1
        down vote



        accepted






        Hint:



        $$dfracsec2y-1tan2y=dfrac1-cos2ysin2y=tan y$$



        Alternatively, $$sqrt2-1=dfracsec2y-1tan2y=csc2y-cot2y$$



        $$iffcsc2y+cot2y=dfrac1csc2y-cot2y=?$$






        share|cite|improve this answer












        Hint:



        $$dfracsec2y-1tan2y=dfrac1-cos2ysin2y=tan y$$



        Alternatively, $$sqrt2-1=dfracsec2y-1tan2y=csc2y-cot2y$$



        $$iffcsc2y+cot2y=dfrac1csc2y-cot2y=?$$







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Aug 17 at 5:21









        lab bhattacharjee

        215k14152264




        215k14152264




















            up vote
            2
            down vote













            HINT:



            Dividing tan theta both side you get - $$frac1-cosxsinx= sqrt2-1$$ Now square it on both sides , and solving further you will reach the solution.



            Additional hints: $$frac1-cosx1+cosx= 3-2sqrt2$$ $$cosx = frac1sqrt2 $$ and you are done.






            share|cite|improve this answer




















            • Are the answers of yours the same of main equation?
              – Nosrati
              Aug 17 at 5:41







            • 3




              two points: 1) division by tan theta deprived of one root; 2) squaring introduced extra root.
              – farruhota
              Aug 17 at 5:58














            up vote
            2
            down vote













            HINT:



            Dividing tan theta both side you get - $$frac1-cosxsinx= sqrt2-1$$ Now square it on both sides , and solving further you will reach the solution.



            Additional hints: $$frac1-cosx1+cosx= 3-2sqrt2$$ $$cosx = frac1sqrt2 $$ and you are done.






            share|cite|improve this answer




















            • Are the answers of yours the same of main equation?
              – Nosrati
              Aug 17 at 5:41







            • 3




              two points: 1) division by tan theta deprived of one root; 2) squaring introduced extra root.
              – farruhota
              Aug 17 at 5:58












            up vote
            2
            down vote










            up vote
            2
            down vote









            HINT:



            Dividing tan theta both side you get - $$frac1-cosxsinx= sqrt2-1$$ Now square it on both sides , and solving further you will reach the solution.



            Additional hints: $$frac1-cosx1+cosx= 3-2sqrt2$$ $$cosx = frac1sqrt2 $$ and you are done.






            share|cite|improve this answer












            HINT:



            Dividing tan theta both side you get - $$frac1-cosxsinx= sqrt2-1$$ Now square it on both sides , and solving further you will reach the solution.



            Additional hints: $$frac1-cosx1+cosx= 3-2sqrt2$$ $$cosx = frac1sqrt2 $$ and you are done.







            share|cite|improve this answer












            share|cite|improve this answer



            share|cite|improve this answer










            answered Aug 17 at 5:35









            Identicon

            42015




            42015











            • Are the answers of yours the same of main equation?
              – Nosrati
              Aug 17 at 5:41







            • 3




              two points: 1) division by tan theta deprived of one root; 2) squaring introduced extra root.
              – farruhota
              Aug 17 at 5:58
















            • Are the answers of yours the same of main equation?
              – Nosrati
              Aug 17 at 5:41







            • 3




              two points: 1) division by tan theta deprived of one root; 2) squaring introduced extra root.
              – farruhota
              Aug 17 at 5:58















            Are the answers of yours the same of main equation?
            – Nosrati
            Aug 17 at 5:41





            Are the answers of yours the same of main equation?
            – Nosrati
            Aug 17 at 5:41





            3




            3




            two points: 1) division by tan theta deprived of one root; 2) squaring introduced extra root.
            – farruhota
            Aug 17 at 5:58




            two points: 1) division by tan theta deprived of one root; 2) squaring introduced extra root.
            – farruhota
            Aug 17 at 5:58












             

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