If θ = c o t - 1 α ,   φ = c o t - 1 β and α β = - 1   α > β , then the value of θ - φ is equal to

Step-by-step solution

∵ cot - 1 α = θ ⇒ α = cot ⁡ θ . . . . . . . . . . . i Also, c o t - 1 β = φ ⇒ β = cot ⁡ φ . . . . . . . . . . . i i Now, given α β = - 1 So, from ( i )   &   ( ii ) , we get, cot ⁡ θ . cot ⁡ φ = - 1 ⇒ tan ⁡ θ tan ⁡ φ = - 1       . . . . . . . . . i i i t a n θ - φ = tan ⁡ θ - tan ⁡ φ 1 + tan ⁡ θ tan ⁡ φ