Problem

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

Solution

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

From Solvely APP
Source: https://solvelyapp.com/problems/19296/

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