Question

show that
cosA/1-tanA + SinA/1-cotA = sinA+cosA


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Answer 1

see the attached document

Answer 2

$\frac{cosA}{1 - tanA} + \frac{sinA}{1 - cotA} \\ \\ = \frac{ {cos}^{2}A }{cosA - sinA} + \frac{ {sin}^{2}A }{sinA - cosA} \\ \\ = \frac{ {cos}^{2} A}{cosA - sinA} - \frac{ {sin}^{2}A }{cosA- sinA} \\ \\ = \frac{ {cos}^{2}A - {sin}^{2} A}{cosA - sinA} \\ \\ = cosA + sinA$