Math, asked by Shibo2509, 5 hours ago

F(x) =sinx and f(x)-f'(x) =0 then find x

Answers

Answered by TrustedAnswerer19
62

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f(x) = sin x

so, f'(x) = d (sin x) / dx = cos x

now,

f(x) - f'(x) =0

 \implies \: sin \: x \:  -  \: \: cos \: x \:  = 0 \\ \implies \:  \: sin \: x \:  =  \: cos \: x \:  \\ \implies \:  \frac{sin \: x}{cos \: x}  = 1 \\ \implies \: tan \: x \:  = 1 \\ \implies \: tan \: x \:  =  \: tan \:  \frac{\pi}{4} \\   \therefore \:  \: x =  \frac{\pi}{4}  = {45}^{ \circ}  \\

Or,

we can write it in another way,

tan \: x =  \: tan \:  \frac{\pi}{4}  \\  \implies \: x = n\pi +  \frac{\pi}{4}  \\  \\ where \:  \:  \:  \: n \in Z \:

Cause we know that,

tan  \: \theta \:  = tan \:  \alpha  \\  \implies \:  \theta = n\pi +  \alpha  \\  where \: \\ n \in \: Z \:

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