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If f(x-y)=f(x).g(y)-f(y).g(x) and g(x-y)...

If `f(x-y)=f(x).g(y)-f(y).g(x)` and `g(x-y)=g(x).g(y)+f(x).f(y)` for all `x in R` . If right handed derivative at x=0 exists for f(x) find the derivative of g(x) at x =0

A

`-1`

B

0

C

1

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
From the given functional relations, we can consider
`f(x)=sin x and g(x) cos x`
`therefore" "g'(x)=-sin x`
`therefore" "g'(0)=0`
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