If Cos A, Sin A, Cot A are in geometric progression, then the value of $Tan^6 A- Tan^2 A$ is :
Answer & explanation
Correct answer: option 4
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