If $cos(x) = sin(y)-cos(z)$, prove that $xyz=frac{pi}{2}$ [closed]












0












$begingroup$


I have no clue where to start from.



I tried to rewrite $sin(y)$ as $cosleft(frac{pi}{2}-yright)$, but don't know what to do next.






trigonometry







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closed as unclear what you're asking by RRL, Shaun, KReiser, Jyrki Lahtonen, José Carlos Santos Dec 28 '18 at 11:18


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.














  • 4




    $begingroup$
    Did you omit some assumption about a relation among $x,y,z$? Are they the angle in triangle or something?
    $endgroup$
    – coffeemath
    Dec 28 '18 at 7:24






  • 2




    $begingroup$
    Also, is it about the product of 3 angles? Probably it's rather meant like a single angle $xyzangle$, that is just $y$. Is that right?
    $endgroup$
    – Berci
    Dec 28 '18 at 8:41
















0












$begingroup$


I have no clue where to start from.



I tried to rewrite $sin(y)$ as $cosleft(frac{pi}{2}-yright)$, but don't know what to do next.






trigonometry







share|cite|improve this question









$endgroup$



closed as unclear what you're asking by RRL, Shaun, KReiser, Jyrki Lahtonen, José Carlos Santos Dec 28 '18 at 11:18


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.














  • 4




    $begingroup$
    Did you omit some assumption about a relation among $x,y,z$? Are they the angle in triangle or something?
    $endgroup$
    – coffeemath
    Dec 28 '18 at 7:24






  • 2




    $begingroup$
    Also, is it about the product of 3 angles? Probably it's rather meant like a single angle $xyzangle$, that is just $y$. Is that right?
    $endgroup$
    – Berci
    Dec 28 '18 at 8:41














0












0








0


0



$begingroup$


I have no clue where to start from.



I tried to rewrite $sin(y)$ as $cosleft(frac{pi}{2}-yright)$, but don't know what to do next.






trigonometry







share|cite|improve this question









$endgroup$




I have no clue where to start from.



I tried to rewrite $sin(y)$ as $cosleft(frac{pi}{2}-yright)$, but don't know what to do next.






trigonometry




trigonometry






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Dec 28 '18 at 7:15









Andrew FountAndrew Fount

7401612




7401612




closed as unclear what you're asking by RRL, Shaun, KReiser, Jyrki Lahtonen, José Carlos Santos Dec 28 '18 at 11:18


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.









closed as unclear what you're asking by RRL, Shaun, KReiser, Jyrki Lahtonen, José Carlos Santos Dec 28 '18 at 11:18


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.










  • 4




    $begingroup$
    Did you omit some assumption about a relation among $x,y,z$? Are they the angle in triangle or something?
    $endgroup$
    – coffeemath
    Dec 28 '18 at 7:24






  • 2




    $begingroup$
    Also, is it about the product of 3 angles? Probably it's rather meant like a single angle $xyzangle$, that is just $y$. Is that right?
    $endgroup$
    – Berci
    Dec 28 '18 at 8:41














  • 4




    $begingroup$
    Did you omit some assumption about a relation among $x,y,z$? Are they the angle in triangle or something?
    $endgroup$
    – coffeemath
    Dec 28 '18 at 7:24






  • 2




    $begingroup$
    Also, is it about the product of 3 angles? Probably it's rather meant like a single angle $xyzangle$, that is just $y$. Is that right?
    $endgroup$
    – Berci
    Dec 28 '18 at 8:41








4




4




$begingroup$
Did you omit some assumption about a relation among $x,y,z$? Are they the angle in triangle or something?
$endgroup$
– coffeemath
Dec 28 '18 at 7:24




$begingroup$
Did you omit some assumption about a relation among $x,y,z$? Are they the angle in triangle or something?
$endgroup$
– coffeemath
Dec 28 '18 at 7:24




2




2




$begingroup$
Also, is it about the product of 3 angles? Probably it's rather meant like a single angle $xyzangle$, that is just $y$. Is that right?
$endgroup$
– Berci
Dec 28 '18 at 8:41




$begingroup$
Also, is it about the product of 3 angles? Probably it's rather meant like a single angle $xyzangle$, that is just $y$. Is that right?
$endgroup$
– Berci
Dec 28 '18 at 8:41










2 Answers
2






active

oldest

votes


















7












$begingroup$

$x=0,y=pi /2,z=pi /2$ is a counterexample.






share|cite|improve this answer









$endgroup$





















    0












    $begingroup$

    Relationship



    $$cos(x)=sin(y)-cos(z) tag{1}$$



    is invariant separately by



    $$x leftrightarrow -x, z leftrightarrow -z, y leftrightarrow pi-y, cdots tag{2}$$



    Thus all relationships that are supposed to be consequences of (1) must be invariant by transformations (2), which is evidently not the case for $xyz=pi/2$.



    Generaly speaking, I don't know any trigonometric formula involving the product of some angles.






    share|cite|improve this answer











    $endgroup$




















      2 Answers
      2






      active

      oldest

      votes








      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      7












      $begingroup$

      $x=0,y=pi /2,z=pi /2$ is a counterexample.






      share|cite|improve this answer









      $endgroup$


















        7












        $begingroup$

        $x=0,y=pi /2,z=pi /2$ is a counterexample.






        share|cite|improve this answer









        $endgroup$
















          7












          7








          7





          $begingroup$

          $x=0,y=pi /2,z=pi /2$ is a counterexample.






          share|cite|improve this answer









          $endgroup$



          $x=0,y=pi /2,z=pi /2$ is a counterexample.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Dec 28 '18 at 7:19









          Kavi Rama MurthyKavi Rama Murthy

          68.3k53169




          68.3k53169























              0












              $begingroup$

              Relationship



              $$cos(x)=sin(y)-cos(z) tag{1}$$



              is invariant separately by



              $$x leftrightarrow -x, z leftrightarrow -z, y leftrightarrow pi-y, cdots tag{2}$$



              Thus all relationships that are supposed to be consequences of (1) must be invariant by transformations (2), which is evidently not the case for $xyz=pi/2$.



              Generaly speaking, I don't know any trigonometric formula involving the product of some angles.






              share|cite|improve this answer











              $endgroup$


















                0












                $begingroup$

                Relationship



                $$cos(x)=sin(y)-cos(z) tag{1}$$



                is invariant separately by



                $$x leftrightarrow -x, z leftrightarrow -z, y leftrightarrow pi-y, cdots tag{2}$$



                Thus all relationships that are supposed to be consequences of (1) must be invariant by transformations (2), which is evidently not the case for $xyz=pi/2$.



                Generaly speaking, I don't know any trigonometric formula involving the product of some angles.






                share|cite|improve this answer











                $endgroup$
















                  0












                  0








                  0





                  $begingroup$

                  Relationship



                  $$cos(x)=sin(y)-cos(z) tag{1}$$



                  is invariant separately by



                  $$x leftrightarrow -x, z leftrightarrow -z, y leftrightarrow pi-y, cdots tag{2}$$



                  Thus all relationships that are supposed to be consequences of (1) must be invariant by transformations (2), which is evidently not the case for $xyz=pi/2$.



                  Generaly speaking, I don't know any trigonometric formula involving the product of some angles.






                  share|cite|improve this answer











                  $endgroup$



                  Relationship



                  $$cos(x)=sin(y)-cos(z) tag{1}$$



                  is invariant separately by



                  $$x leftrightarrow -x, z leftrightarrow -z, y leftrightarrow pi-y, cdots tag{2}$$



                  Thus all relationships that are supposed to be consequences of (1) must be invariant by transformations (2), which is evidently not the case for $xyz=pi/2$.



                  Generaly speaking, I don't know any trigonometric formula involving the product of some angles.







                  share|cite|improve this answer














                  share|cite|improve this answer



                  share|cite|improve this answer








                  edited Dec 28 '18 at 9:10

























                  answered Dec 28 '18 at 9:04









                  Jean MarieJean Marie

                  30.8k42154




                  30.8k42154















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