SOLUTION: 22. verify the identity csc(-x)/sec(-x)=-cot x

Question 169978: 22. verify the identity csc(-x)/sec(-x)=-cot x
Found 2 solutions by jim_thompson5910, jojo14344:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Note: I'm ONLY manipulating the left side. I'm showing the right side for comparison

Start with the given equation

Use the identities and to get the left side in terms of sine and cosine

Multiply the first fraction by the reciprocal of the second fraction.

Combine and multiply the fractions.

Use the identity

Use the identity

Reduce

Use the identity
Answer by jojo14344(1513) (Show Source): You can put this solution on YOUR website!

Re-writing:
Via Reciprocal Identites: ;
Subst. & becomes:

Via Quotient Identities:
Subst. & becomes:

Thank you,
Jojo
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