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Chapter 5: Problem 2

Verify each identity. $$\cos x \csc x=\cot x$$

Short Answer

Expert verified
Yes, this identity is verified as both sides simplify to \(\cot x\).

Step by step solution

01

Break Down the Trigonometric Identities

Start by expressing all terms in terms of sine and cosine. Therefore, this equation becomes \(\cos x \cdot (1/ \sin x)= \cos x / \sin x\), which simplifies to \(\cos x / \sin x\).
02

Reconverting to Original Trigonometric Functions

Now, reconvert the expression obtained in step 1 back to its original trigonometric notation, meaning \(\cos x / \sin x = \cot x\).
03

Confirm the Identity

With both sides of the equation now simplified to \(\cot x\), you can see that they are equal. This confirms the identity.

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