Question

Find cot x if sin x cot x csc x = square root of two

Answer 1

$\text{Given: } sin(x) cot(x) cosec(x) = \sqrt{2}$
$\text{Find: } cot(x)$

$\text{Important identity: } \boxed{cosec(x) = \frac{1}{sin(x)}}$

$sin(x) cot(x) cosec(x) = sin(x) cot(x) \frac{1}{sin(x)} = \sqrt{2}$
$\therefore cot(x) = \sqrt{2}$