Resposta:
1.
Explicação passo-a-passo:
Vamos usar a regra de Sarrus:
[tex]\begin{vmatrix}\sin x & \sin x & \cot x\\\cos x & \cos x & -1\\0 & \sin x & \tan x\end{vmatrix} =(\sin x\cdotp \cos x\cdotp \tan x) +0+(\cot x\cdotp \cos x\cdotp \sin x) -[ 0+(\sin x\cdotp \cos x\cdotp \tan x)( -1\cdotp \sin x\cdotp \sin x)] \\ \\ =\left(\sin x\cdotp \cancel{\cos x} \cdotp \frac{\sin x}{\cancel{\cos x}}\right) +\left(\frac{\cos x}{\cancel{\sin x}} \cdotp \cos x\cdotp \cancel{\sin x}\right) -\left[\left(\sin x\cdotp \cancel{\cos x} \cdotp \frac{\sin x}{\cancel{\cos x}}\right) -\sin^{2} x\right] \\ =\sin^{2} x+\cos^{2} x-\left(\cancel{\sin^{2} x-\sin^{2} x}\right) =\boxed{\boxed{1}}[/tex]
