Statement (A) : If we know one trigonometric ratio then we can find all trigonometric ratios

Statement (B) : If  $\tan \theta =x$ then  $\text{cot}\theta =\frac{1}{x}$ 

Yes, all trigonometric ratios are inter related to each other.

For example take  $\sin \theta =\frac{3}{5}$

i.e., $\sin \theta =\frac{3}{5}=\frac{\text{Opposite\hspace{0.17em}side\hspace{0.17em}to\hspace{0.17em}}\theta }{\text{Hypotenuse}}$

By Pythagorean theorem,

 $A{C}^2=A{B}^2+B{C}^2$

$5^2=3^2+B{C}^2$

$25=9+B{C}^2$

$B{C}^2=25-9=16$

$BC=\sqrt{16}$

$BC=4$

$\therefore \cos \theta =\frac{BC}{AC}=\frac{4}{5}$

$\text{tan}\theta =\frac{AB}{BC}=\frac{3}{4}$

$\text{cot}\theta =\frac{BC}{AB}=\frac{4}{3}$

$\sec \theta =\frac{AC}{BC}=\frac{5}{4}$

$\text{cosec}\theta =\frac{AC}{AB}=\frac{5}{3}$

$\tan \theta$and  $\cot \theta$are reciprocal to each other.

So, if  $\tan \theta =x$then

$\text{cot}\theta =\frac{1}{\tan \theta }=\frac{1}{x}$