Question

please answer these two questions:
and it is a humble request, please answer only with reference to an image.
else leave the question. ​

Answer 1

Step-by-step explanation:

$\sf \frac{ {cos}^{3}A + {sin}^{3}A}{cosA + sinA } + \frac{ {cos}^{3}A - {sin}^{3}A}{cosA - sinA } \\ \\ \sf = \frac{(cosA + sinA )({sin}^{2}A - sinAcosA + {cos}^{2}A}{cosA + sinA} + \frac{(cosA - sinA )({sin}^{2}A + sinAcosA + {cos}^{2}A}{cosA + sinA} \\ \\ \sf =2( {sin}^{2}A + {cos}^{2}A) \\ \\ \sf = 2 \\ \\ \sf = R.H.S \\ \\ \sf Hence\:proved \\ \\ \sf \frac{tanA}{1 -cotA} + \frac{cotA}{1-tanA}$

Answer 2

Answer:

$\begin{lgathered}\sf \frac{ {cos}^{3}A + {sin}^{3}A}{cosA + sinA } + \frac{ {cos}^{3}A - {sin}^{3}A}{cosA - sinA } \\ \\ \sf = \frac{(cosA + sinA )({sin}^{2}A - sinAcosA + {cos}^{2}A}{cosA + sinA} + \frac{(cosA - sinA )({sin}^{2}A + sinAcosA + {cos}^{2}A}{cosA + sinA} \\ \\ \sf =2( {sin}^{2}A + {cos}^{2}A) \\ \\ \sf = 2 \\ \\ \sf = R.H.S \\ \\ \sf Hence\:proved \\ \\ \sf \frac{tanA}{1 -cotA} + \frac{cotA}{1-tanA}\end{lgathered}$