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

1.	Find the value of (p + q)2, if p + q Cot3 α = Cot α.Cosec α and q = p tan α.1). 1 + Cos α2). 1 + Sin 2α3). 1 – cos 2α4). 1 - Sin α
Answer» p + q COT³α = Cot α.Cosec α ⇒ p + q COS³α/Sin³ α = Cos α/Sin²α Putting q = p TAN α in the equation we get ⇒ p + p tan α.(Cos³α/Sin³ α) = Cos α/Sin²α Putting tan α = sin α /cos α and simplifying we get ⇒ p(1 + Cos²α/Sin²α ) = Cos α/Sin²α ⇒ 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

Find the value of (p + q)2, if p + q Cot3 α = Cot α.Cosec α and q = p tan α.1). 1 + Cos α2). 1 + Sin 2α3). 1 – cos 2α4). 1 - Sin α

Answer»

p + q COT³α = Cot α.Cosec α

⇒ p + q COS³α/Sin³ α = Cos α/Sin²α

Putting q = p TAN α in the equation we get

⇒ p + p tan α.(Cos³α/Sin³ α) = Cos α/Sin²α

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

⇒ p(1 + Cos²α/Sin²α ) = Cos α/Sin²α

⇒ 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