If `"cosec"^(4) theta-"cosec"^(2) theta=1.24," then cot"^(4) theta+cot^2 theta=?`

Options

A. 1.24
B. 1.86
C. 2.48
D. 0.62

Answer

To solve the equation given in the question, we start with the expression:

\[ \csc^4 \theta - \csc^2 \theta = 1.24 \]

### Step 1: Rewrite the equation in terms of cotangent.
We know that:

\[ \csc^2 \theta = 1 + \cot^2 \theta \]

Substituting this into the equation gives:

\[ \csc^4 \theta = (\csc^2 \theta)^2 = (1 + \cot^2 \theta)^2 \]

### Step 2: Expand the squared term.
Now, we can expand \((1 + \cot^2 \theta)^2\):

\[ (1 + \cot^2 \theta)^2 = 1 + 2\cot^2 \theta + \cot^4 \theta \]

### Step 3: Substitute back into the equation.
Now we substitute this back into our original equation:

\[ 1 + 2\cot^2 \theta + \cot^4 \theta - (1 + \cot^2 \theta) = 1.24 \]

### Step 4: Simplify the equation.
This simplifies to:

\[ 1 + 2\cot^2 \theta + \cot^4 \theta - 1 - \cot^2 \theta = 1.24 \]

Which further simplifies to:

\[ \cot^4 \theta + \cot^2 \theta = 1.24 \]

### Step 5: Final expression.
Thus, we find that:

\[ \cot^4 \theta + \cot^2 \theta = 1.24 \]

### Conclusion
The value of \(\cot^4 \theta + \cot^2 \theta\) is:

\[ \boxed{1.24} \]