I've Told You The Answer Already

Since answer to this question is unique and we have to find $\cos x$ when answer is $\sin x$ . Therefore this is posible only when both are same: $\large \color{#D61F06}{\sin x}=\color{#3D99F6}{\cos x}$ $1=\color{#D61F06}{\sin^2 x}+\color{#3D99F6}{\cos^2 x}=2\color{#D61F06}{\sin^2 x}=2\color{#3D99F6}{\cos^2 x}$ $\large \implies \color{#D61F06}{\sin x}=\color{#3D99F6}{\cos x}=\pm \dfrac{1}{\sqrt 2}$

$\sin x=\cos x \Rightarrow \tan x=1 \Rightarrow \sec x = \sqrt{1^2+1}=\pm\sqrt{2} \Rightarrow \cos x=\pm\dfrac{1}{\sqrt{2}}$

$OR$

$\sin^2 x+ \cos^2 x = 1 \Rightarrow 2\cos^2 x =1 \Rightarrow \cos^2 x = \dfrac{1}{2} \Rightarrow \cos x = \pm\dfrac{1}{\sqrt{2}}$

(Liked) This should be a logic question. Nice one!

sin x = cos x : if : x = 45 , so : sin ( - 45 ) = - sin 45 , cos ( - 45 ) = cos 45 .

Dude it was a good one. Good question