Question

The value of \( 2 \tan^{-1} x - \left( \text{cosec} \, \tan^{-1} x - \tan \, \cot \, x \right) \)

• A. \( \tan^{-1} x \)
• B. \( \tan x \)
• C. \( \cot x \)
• D. \( \text{cosec}^{-1} x \)

Hint:

Inverse trigonometric identities can be simplified by using basic algebraic operations and known formulas.

Answer 1

The Correct Option is A

Step 1: Simplifying the expression.
The expression involves inverse trigonometric identities. Using standard trigonometric simplifications, we find that the value of the expression simplifies to \( \tan^{-1} x \).

Step 2: Conclusion.
The correct value is \( \tan^{-1} x \), corresponding to option (1).