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if sinxcosy{f(2x+2y)-f(2x-2y)}=sinycosx{f(2x+2y)+f(2x-2y)} then find relations between f"(x) and f'(x)

if sinxcosy{f(2x+2y)-f(2x-2y)}=sinycosx{f(2x+2y)+f(2x-2y)}
then find relations between f"(x) and f'(x)

Grade:11

1 Answers

Rathod Shankar AskiitiansExpert-IITB
69 Points
9 years ago

simply use componendo-dividendo and get

f(2x+2y)  =  sin(x+y)

f(2x-2y)       sin(x-y)

 

hence your function is f(x) = sin(x/2)

 

:)

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