Question

Verify the identity. Step by step please.

cot^5x=cot^3x csc^2x-cot^3x

Answer 1

divide by cot^3 on both sides

Answer 2

RHS = cot^3(x)csc^2(x) - cot^3(x)
= cot^3(x) (csc^2(x) - 1)
Those would be the first 2 steps. Starting with the right hand side, I factored out the common cot^3(x) to turn the 2 terms into 1.
Now, if you remember your trig identities, you should be able to simplify the brackets in your next step, which should quickly lead you to the left hand side result.

Answer 3

Remember:
1 + tan^2(x) = sec^2(x)
1 + cot^2(x) = cosec^2(x)
sin^2(x) + cos^2(c) = 1
tan(x) = sin(x)/cos(x)

You only have to use one of those for your identity. Which one do you think it would be?
[Hint: you may need to do some rearranging]

Answer 4

Thank you! You are a life saver!

Answer 5

No problem :)