Factor the trigonometric expression completely.
\[
\csc ^{2} w-\tan ^{2} x
\]
\[
\csc ^{2} w-\tan ^{2} x=(\csc w-\square)(\square+\tan x)
\]

Answer

Expert–verified

Hide Steps

Answer

Final Answer: The factored form of the given trigonometric expression is \(\boxed{(\csc w - \tan x)(\csc w + \tan x)}\)

Steps

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 \(\boxed{(\csc w - \tan x)(\csc w + \tan x)}\)