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## Homework Statement

Verify that [itex]\frac{cosθ}{1-tanθ}[/itex] + [itex]\frac{sinθ}{1-cotθ}[/itex] = sinθ + cosθ is an identity.

## Homework Equations

- Reciprocal Trigonometric Identities

- Pythagorean Trig Identities

## The Attempt at a Solution

Every time I try to manipulate the LHS of the equation I always get -1 and as far as I know, the sum of sine and cosine always has to be both squared to get 1. But in this case, the RHS has sinθ + cosθ. Is it possible for sinθ + cosθ to equal 1? Or I just made the wrong way of manipulating in LHS? Thank you!

PS: A hint for the problem will do. I would love to show my work from what I will have to learn from your replies.