Question

Prove that cosA/1-tanA + sinA/1-cotA =cosA+sinA​

Answer 1

Step-by-step explanation:

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Answer 2

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