Question

Prove that : ${\cot }^{2}A-{\cos }^{2}A={\cos }^{2}A.{\cot }^{2}A$

Answer 1

${\cot }^{2}A-{\cos }^{2}A={\cos }^{2}A\cdot {\cot }^{2}A$

$\Rightarrow \frac{{\cos }^{2}A}{{\sin }^{2}A}-{\cos }^{2}A$

$\Rightarrow {\cos }^{2}A\frac{(1-{\sin }^{2}A)}{{\sin }^{2}A}$

$\Rightarrow {\cos }^{2}A\cdot \frac{{\cos }^{2}A}{{\sin }^{2}A}$

$\Rightarrow {\cos }^{2}A\cdot {\cot }^{2}A=$RHS

Hence proved.