Question

The formula $\cos ^ { - 1 } \frac { 1 - x ^ { 2 } } { 1 + x ^ { 2 } } = 2 \tan ^ { - 1 } x$ holds only for

• A. $x \in R$
• B. $| x | \leq 1$
• C. $x \in ( - 1,1 ]$
• D. $x \in [ 1 , + \infty )$

Answer 1

Answer: (D)

$x \in [ 1 , + \infty )$

Answer 2

If $2 \times \left( - \frac { \pi } { 2 } \right)$. So, the fomula does not hold.

If $x < - 1$ the angle on the LHS is in the second quadrant while the angle on the RHS is $x > 1$ the angle on the LHS is in the second quadrant while the angle on the RHS is $2 \times$ (angle in the first quadrant) and these two may be equal.

If $- 1 < x < 0$, the angle on the LHS is positive and that on the RHS is negative and the two cannot be equal