If cos B , sin B, cot B are in geometric progression, then the value of tan6B - tan2 B is?
Answer & explanation
Correct answer: option 1
A, B, C are in g. p. ⇒ B2 = AC
sin2 B = cos B × cot B = cos B × \(\frac{cos B}{sin B}\)
sin3 B = cos2 B
divide both side by cos3 B
tan3 B = sec B
(tan3 B)2 = sec2 B
tan6 B = 1 + tan2 B
tan6 B - tan2 B = 1