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(sinx)3-(cosx)3=[(sinx)2-(cosx)2][1-2*(sinx)2*(cosx)2] here (sinx)3 means cube of sinx and similarly other powers .


(sinx)3-(cosx)3=[(sinx)2-(cosx)2][1-2*(sinx)2*(cosx)2]


here (sinx)3 means cube of sinx and similarly other powers .


Grade:12

1 Answers

vikas askiitian expert
509 Points
10 years ago

(sinx)3 -(cosx)3 = (sinx-cosx)(sin2 x +cos2 x -sinxcosx) or     (sinx+cosx)(1-sin2x/2)

sin2 x -cos2 x =(sinx-cosx)(sinx+cosx)

on putting these

we get

          (sinx+cosx)(1-sin2x/2 ) = ((sinx+cosx)(sinx-cosx)(1-2(sinxcosx)2 )         or

 (sinx+cosx) {1-sin2x/2 - (sinx-cosx)(1-2(sinxcosx)2 } = 0

 sinx +cosx =0                            or                  {1-sin2x/2 -(sinx-cosx)(1-2(sinxcosx)2 }=0

 tanx=-1                                    or            {1-sin2x/2  -(sinx-cosx)(1-(sin2x)2 /2 ) =0

x =npi -pi/4                               or           (sinx-cosx)2 =1-sin2x ,so nw sustitute the value of sin2x in above eq                 

                                                       & simplify it...

 

 

 

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