Question

tan square A minus sin square A×tan square A sin square A​

Answer 1

tan^2 A = sin^2 A / cos^2 A

Therefore, tan^2 A - sin^2 A = sin^2 A * ((1/cos^2 A) - 1)

= sin^2 A * ((1 - cos^2 A) / cos^2 A)

= (sin^2 A / cos^2 A) * Sin^2 A —- 1 - cos^2 A = sin^2 A

= (tan^2 A) * (sin^2 A) —- sin^2 A / cos^2 A = tan^2 A

We started with tan^2 A - sin^2 A and arrived at (tan^2 A) * (sin^2 A), by logically following the standard conversions.

Thus, it is proved that tan^2 A - sin^2 A = (tan^2 A) * (sin^2 A).