If -π2<θ<π2 and θ≠π4, then the value of cotπ4+θcotπ4-θ is
0
-1
1
2
Explanation for the correct option:
Step-1: Apply the formulas
cotθ=1tanθ and tan(A-B)=tanA-tanB1+tanAtanB
Given condition -π2<θ<π2and θ≠π4
Consider cotπ4+θcotπ4-θ
Step 2: Find the value of cotπ4+θcotπ4-θ
∴cotπ4+θcotπ4-θ=1tanπ4+θ1tanπ4-θ;∴cotθ=1tanθ=1tanπ4+tanθ1-tanπ4tanθ1tanπ4-tanθ1+tanπ4tanθ;∵tan(A-B)=tanA-tanB1+tanAtanB=1-tanπ4tanθtanπ4+tanθ1+tanπ4tanθtanπ4-tanθ
we know tanπ4=1
∴cotπ4+θcotπ4-θ=1-tanθ1+tanθ1+tanθ1-tanθ=1
Therefore, the value of cotπ4+θcotπ4-θ = 1
Hence, the correct answer is option (C)