Question

If f(x)=2x/1+x^2 show that f(tanthita)=sin2thita

Answer 1

$\huge\boxed{\underline{\underline{\green{\tt Solution}}}} </p><p>$

We know that

$\frac{2tan \theta}{1 + {tan}^{2} \theta} = sin2\theta$

Now

$f(x) = \frac{2x}{1 + {x}^{2} }$

So

$f(tan \theta) = \frac{2tan \theta}{1 + {tan}^{2} \theta} = sin2\theta$

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