Question

plz find the ANS
please

Answer 1

hope this will help u.. :-)

Answer 2

$Given : \frac{tanA}{1 - cotA} + \frac{cotA}{1 - tanA}$

$=> \frac{tanA}{1 - \frac{cosA}{sinA}}+\frac{cotA}{1 -  \frac{sinA}{cosA}}$

$=> \frac{sinA * sinA}{cosA(sinA - cosA)} +\frac{cosA * cosA}{sinA(cosA - sinA)}$

$=> \frac{sin^2A}{cosA(sinA - cosA)}-\frac{cos^2A}{sinA(sinA - cosA)}$

$=> \frac{sin^3A - cos^3A}{sinA * cosA(sinA - cosA)}$

We know that a^3 - b^3 = (a - b)(a^2 + ab + b^2)

$=> \frac{(sinA - cosA)(sin^2A + sinAcosA + cos^2A)}{sinA * cosA(sinA - cosA)}$

$=> \frac{1 + sinAcosA}{sinAcosA}$

$=> \frac{1}{sinAcosA}+\frac{sinAcosA}{sinAcosA}$

$=> \frac{1}{sinAcosA} + 1$

$=> \frac{1}{sinA}+\frac{1}{cosA}+1$

⇒ cosecA secA + 1

Hope it helps!