Question

question
the expression 12 - 12 csc² x is equivalent to
answer
-12 sin² x
-12 tan² x
-12 sec² x
-12 sin² x
12 sin² x
12 tan² x
12 sec² x
-12
12 cos² x
-12 csc² x
12 csc² x
12 cot² x
-12 cot² x
12

Explanation:

Step1: Use the Pythagorean identity

Recall the Pythagorean identity \(1+\cot^{2}x=\csc^{2}x\).

Step2: Rearrange the identity

We can rewrite it as \(\cot^{2}x=\csc^{2}x - 1\).

Step3: Substitute into the given expression

Given \(12-12\csc^{2}x\), factor out \(- 12\): \(12-12\csc^{2}x=-12(\csc^{2}x - 1)\).

Step4: Replace \(\csc^{2}x - 1\)

Since \(\csc^{2}x - 1=\cot^{2}x\), then \(-12(\csc^{2}x - 1)=-12\cot^{2}x\).

Answer:

\(-12\cot^{2}x\)