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Let f(x) and g(x) be differentiable fun...

Let ` f(x) and g(x)` be differentiable functions such that `f(x)+ int_(0)^(x) g(t)dt= sin x(cos x- sin x) and (f'(x))^(2)+ (g(x))^(2) = 1,"then" f(x) and g (x) ` respectively , can be

A

`(1)/(2) sin 2x, sin 2 x `

B

`( cos2x)/(2), cos 2 x`

C

`(1)/(2) sin 2 x, - sin 2x`

D

`-sin ^(2) x, cos 2 x `

Text Solution

Verified by Experts

The correct Answer is:
C
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