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The correct option is B.
$$sin x + cos x =\sqrt{2} sin x$$
$$\Rightarrow$$ $$cos x = \sqrt{2} sin x - sin x$$ = ($$\sqrt{2} - 1$$) $$sinx$$
$$\Rightarrow$$ $$tan x = \frac{1}{\sqrt2-1}$$ = $$\sqrt{2}+1$$
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