Question

Prove that, cot ²A +1 = cosec² A​

Answer 1

Answer:

${cot}^{2} a + 1 = {cosec}^{2}a \\ \\ l.h.s. \\ {cot}^{2} a + 1 \\ = \frac{1}{ {tan}^{2}a } + 1 \\ = \frac{1 + {tan}^{2} a}{ {tan}^{2} a} \\ = {sec}^{2} a \div {tan}^{2} a \\ = \frac{1}{ {cos}^{2}a } \times \frac{ {cos}^{2}a }{ {sin}^{2} a} \\ \\ = \frac{1}{ {sin}^{2}a } \\ = {cosec}^{2} a$

Hence L. H. S. = R. H. S (proved)