Question

please answer this question

Answer 1

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

$\frac{sinA}{ \frac{cosA}{1 - \frac{cosA}{sinA} } } + \frac{cosA}{ \frac{sinA}{1 - \frac{sinA}{cosA} } }$

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

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

$\frac{sin^3A - cos^3A}{cosAsinA(sinA-cosA))}$

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

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

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

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

$\frac{1}{cosA} * \frac{1}{sinA} + \frac{sinAcosA}{sinAcosA}$

secA * cosecA + 1.



Hope this helps!