Published by:
CGP EDU Academic Team
Published on: August 13, 2026
The sum of absolute value of all possible values of x for which cos tan − 1 sin cot − 1 x = 
.
Text Solution
Verified by ExpertsThe correct answer is:
30
(30)
Sol. Case-I : x ≥ 0
Let cot –1 x = θ
∴ θ ∈ 
⇒ x = cot θ
∴ sin θ = 
⇒ sin –1 sin θ = sin –1 
⇒ θ = sin –1 
Case-II : x < 0
Let cot –1 x = θ
∴ θ ∈ 
⇒ cot θ = x
∴ sin θ = 
⇒ sin –1 sin θ = sin –1 
⇒ π – θ = sin –1 
⇒ θ = π – sin –1 
Therefore,
LHS = 
= cos tan –1 sin sin –1 
; x ∈ R = cos tan –1 
Let φ = tan –1 
As 
∈ (0, 1] ∴ φ ∈ 
∴ tan φ = 
∴ cos φ = 
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