Statement -1: If a is twice the tangent of the arithmetic mean of `sin^(-1)x and cos^(-1)` x , b the geometric mean of tanx and cot x then `x^(2)-ax+b=0rarr x=1` statement-2: `tan((sin^(-1)x+cos^(-1)x)/(2))=1`

Options

A. Statement-1 is is True, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is True.

Explanation

To solve the problem step by step, we will analyze both statements provided and derive the necessary values.

### Step 1: Analyzing Statement 1

**Statement 1**: If \( a \) is twice the tangent of the arithmetic mean of \( \sin^{-1} x \) and \( \cos^{-1} x \), and \( b \) is the geometric mean of \( \tan x \) and \( \cot x \), then the equation \( x^2 - ax + b = 0 \) has a solution \( x = 1 \).

1. **Finding \( a \)**:
- The arithmetic mean of \( \sin^{-1} x \) and \( \cos^{-1} x \) is given by:
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