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# In right triangle $ABC$, right angled at $C,$ if $\tan A = 1,$ then the value of $2 \sin A \cos A$ is

$\begin{array}{1 1}(A) \; 1 \\(B)\;2 \\(C)\;0 \\(D)\;-1 \end{array}$

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Solution :
Let BC = k and AC = k
$AB= \sqrt {(k)^2+(k)^2}$
$\quad= \sqrt {k^2+k^2}$
=> $AB = \sqrt {2k^2}$
$\qquad= \sqrt {2k}$
$\theta$
$2 \sin A \cos A = 2 \times \large\frac{k}{\sqrt 2 k} \times \frac{k}{\sqrt 2 k}$
$\qquad = 2 \times \large\frac{1}{2}$
$\qquad= 1$