Problem 2
Question
Verify each identity. $$\cos x \csc x=\cot x$$
Step-by-Step Solution
Verified Answer
Yes, this identity is verified as both sides simplify to \(\cot x\).
1Step 1: 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 \(\cos x / \sin x\).
2Step 2: Reconverting to Original Trigonometric Functions
Now, reconvert the expression obtained in step 1 back to its original trigonometric notation, meaning \(\cos x / \sin x = \cot x\).
3Step 3: 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.
Other exercises in this chapter
Problem 2
Be sure that you've familiarized yourself with the first set of formulas presented in this section by working \(1-4\) in the Concept and Vocabulary Check. Use t
View solution Problem 2
Use substitution to determine whether the given \(x\) -value is a solution of the equation. $$\tan x=\sqrt{3}, \quad x=\frac{\pi}{3}$$
View solution Problem 2
Find the exact value of each expression.. $$\cos \left(120^{\circ}-45^{\circ}\right)$$
View solution Problem 3
Be sure that you've familiarized yourself with the first set of formulas presented in this section by working \(1-4\) in the Concept and Vocabulary Check. Use t
View solution