Prove that

Asked by Rahulsinha1993 | 8th Jul, 2010, 03:06: PM

Expert Answer:

Dear Student,
 
Differentiate the given expression using division rule to get:
dy/dx = {[(cos x + sin x)×(-sinx-cosx)] - [(cos x - sin x)×(-sinx + cosx)]} / (cosx+sinx)2
=> dy/dx = [-(cosx+sinx)2 - (cosx-sinx)2] / (cosx+sinx)2
=> dy/dx = -1 - (cosx-sinx)2 / (cosx+sinx)2
=> dy/dx = -1 - y2
=> dy/dx+1+y2 = 0
HenceProved
 
Regards Topperlearning.

Answered by  | 14th Jul, 2010, 01:51: PM

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