Step 1 :Factor the trigonometric expression completely: \(\csc ^{2} w-\tan ^{2} x\)
Step 2 :Use the difference of squares formula: \(a^2 - b^2 = (a - b)(a + b)\)
Step 3 :Apply the formula to the given expression: \(\csc ^{2} w-\tan ^{2} x=(\csc w-\tan x)(\csc w+\tan x)\)
Step 4 :Final Answer: The factored form of the given trigonometric expression is \(\boxed{(\csc w - \tan x)(\csc w + \tan x)}\)