Question

Prove that $tan ^{2} A.cos ^{2} A=1-cos ^{2} A$

Answer 1

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

Answer 2

$tan^2A\cdot cos^2A=1-cos^2A\\\\L=\frac{sin^2A}{cos^2A}\cdot cos^2A=sin^2A\\\\R=1-cos^2A=sin^2A\\\\L=R\\--------------------\\tanx=\frac{sinx}{cosx}\\\\sin^2x+cos^2x=1\to sin^2x=1-cos^2x$