If Cos A, Sin A, Cot A are in geometric progression, then the value of $Tan^6 A- Tan^2 A$ is :

1

Cos A, Sin A, Cot A are in geometric progression

So,

sin²A = cosA . cotA

sin²A = cosA . \(\frac{cosA}{sinA}\)

sin³A = cos²A

( divide both  side by cos³A )

⇒ tan³A = secA

( on squaring both sides )

tan6 A = sec²A

Now,

tan6 A - tan²A

= sec²A - tan²A          ( sec²A - tan²A = 1 )

= 1