If `sqrt((sec^(2)A-1))=x` , then the value of x is

Options

A. cot A
B. tan A
C. cosec A sec A
D. cos A

Answer

To solve the equation \( \sqrt{\sec^2 A - 1} = x \), we can follow these steps:

### Step 1: Use the identity for secant
We know from trigonometric identities that:
\[ \sec^2 A = 1 + \tan^2 A \]
This means we can rewrite \( \sec^2 A - 1 \) as:
\[ \sec^2 A - 1 = \tan^2 A \]

### Step 2: Substitute into the equation
Now, substituting this into our original equation gives:
\[ \sqrt{\sec^2 A - 1} = \sqrt{\tan^2 A} \]

### Step 3: Simplify the square root
The square root of \( \tan^2 A \) is:
\[ \sqrt{\tan^2 A} = |\tan A| \]
Thus, we can express \( x \) as:
\[ x = |\tan A| \]

### Final Answer
Therefore, the value of \( x \) is:
\[ x = |\tan A| \]

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