If CosA, SinA, CotA are in geometric progression, then the value of Tan6A – Tan2A is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e 1
| Understanding | Application |
| We will use the properties of G.P. to simplify the problem. |
CosA, SinA & CotA are in G.P. so, ⇒ Sin2A = CosA × CotA ⇒ Sin3A = Cos2A Divide both sides by Cos3A (We want to convert to Tan3A) ⇒ Tan3A = SecA ⇒ Tan6A = Sec2A |
| We will now use trigonometric basic identities to transform the equation in a known format. |
⇒ Tan6A – Tan2A ⇒ Sec2A - Tan2A We know that Sec2A - Tan2A = 1 ⇒ 1 |