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PRACHI MISHRA Grade: 12
        


(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 .


6 years ago

Answers : (1)

vikas askiitian expert
510 Points
										

(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...


 


 


 

6 years ago
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