Question

Prove that 1+cot^2 A = cosec^2 A​

Answer 1

Answer:

$1 + {cot}^{2} a = \cosec ^{2} a \\ \\ take \: l.h.s \\ \\ 1 + \frac{cos ^{2} a}{sin ^{2} a} \\ \\ \frac{sin ^{2} a + cos^{2} a}{sin ^{2} a} \\ \\ we \: know \: that \: \\ \\ cos ^{2} a + sin ^{2} a = 1 \\ \\ so, \\ \\ \frac{1}{sin ^{2} a} \\ \\ cosec ^{2} a \\ \\ hence \: proved \: l.h.s = r.h.s$