Let `l= sin theta, m=cos theta and n=tan theta`.
Q. If `theta=-1042^(@)`, then :

Options

A. `n gt 1`
B. `n lt 1`
C. `n=1`
D. nothing can be said

Answer

To solve the problem, we need to evaluate the trigonometric functions given that \(\theta = -1042^\circ\). We will follow these steps:

### Step 1: Normalize the Angle
To find equivalent angles in the standard range, we can add or subtract multiples of \(360^\circ\).

\[ \theta = -1042^\circ + 3 \times 360^\circ \]

Calculating this gives:

\[ \theta = -1042 + 1080 = 38^\circ \]

### Step 2: Calculate the Trigonometric Functions
Now that we have \(\theta = 38^\circ\), we can find the values of \(l\), \(m\), and \(n\):

1. **Calculate \(l = \sin \theta\)**:
\[ l = \sin(38^\circ) \]

2. **Calculate \(m = \cos \theta\)**:
\[ m = \cos(38^\circ) \]

3. **Calculate \(n = \tan \theta\)**:
\[ n = \tan(38^\circ) \]

### Step 3: Analyze the Value of \(n\)
We know that \(\tan(45^\circ) = 1\) and that the tangent function decreases as the angle decreases from \(45^\circ\). Since \(38^\circ < 45^\circ\), we can conclude:

\[ n = \tan(38^\circ) < 1 \]

### Conclusion
Thus, the conclusion is that \(n\) is less than 1.

### Final Answer
The correct statement is that \(n < 1\).

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