SOLUTION: This is a Trigonometric Identity Problem. Simplify the expression: csc(-x)-csc(-x)cos^2(x) I think that the two csc(-x)s cancel out to leave the answer being cos^2(x) but I'

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Question 307231: This is a Trigonometric Identity Problem.
Simplify the expression: csc(-x)-csc(-x)cos^2(x)
I think that the two csc(-x)s cancel out to leave the answer being cos^2(x) but I'm not sure since they are multiplied.
Please confirm my answer.
Thanks!
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
Rules for trig functions of negative values:

The cosine and secant are the only even trig functions,
and the negative sign "disappears":




All the other trig functions are odd trig functions,
and the negative sign comes out in front:






csc(-x)-csc(-x)cos2(x) becomes

-csc(x)-[-csc(x)]cos2(x) 

-csc(x)+csc(x)cos2(x)

Factor out -csc(x)

-csc(x)[1-cos2(x)]

Us the identity  written as  to replace the bracketed expression:

-csc(x)sin2(x)

Use the identity  to replace the cosecant factor:

-sin2(x)

This simplifies to

-sin(x)

Edwin
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