Question

If sinθ, cosθ and tan θ are in GP, then cot⁵ θ cot²θ − is equal to

(A)  cosec² θ

(B)   cosecθ

(C)  1 

(D)  0

Answer 1

Correct option (C)  1 

Given sin θ , cos θ and tan q are in GP. This means

cos²  θ  = sin² θ /cos θ ⇒ sin²θ = cos³θ ⇒ cosec ⇒ = cot³ θ

Now,

cot⁶ θ - cot² θ = cosec²  θ cot² θ = 1