Find the value of (p + q)2, if p + q Cot3 α = Cot α.Cosec α and q = p tan α.

p + q Cot3 α = Cot α.Cosec α

⇒ p + q Cos3 α/Sin3 α = Cos α/Sin2 α

Putting q = p tan α in the equation we get

⇒ p + p tan α.(Cos3 α/Sin3 α) = Cos α/Sin2 α

Putting tan α = sin α /cos α and simplifying we get

⇒ p(1 + Cos2 α/Sin2 α ) = Cos α/Sin2 α

⇒ p = Cos α

Putting that in q = p tan α we get q = Sin α

Here (p + q)2 = (Sin α + Cos α)2

Using (a + b)2 = a2 + b2 + 2ab we get

(p + q)2 = Sin2 α + Cos2 α + 2 Sin α.Cos α

Using Sin2 α + Cos2 α = 1 and 2 Sin α.Cos α = Sin 2α

We get (p + q)2 = 1 + Sin 2α