Question

Prove that ${\csc }^{2}A-{\cot }^{2}A=1$ where $0\le A\le {90}^o$

Answer 1

Given expression $\cos e{c}^{2}A={\cot }^{2}A$

$=\frac{1}{\sin A}-\frac{{\cos }^{2}A}{{\sin }^{2}A}$

$=\frac{1-{\cos }^{2}A}{{\sin }^{2}A}$

$=\frac{{\sin }^{2}A}{{\sin }^{2}A}$

$=1$