Let `l= sin theta, m=cos theta and n=tan theta`.
Q. If `theta=-1042^(@)`, then : (a)`n>1` (b) `n<1` (c) `n=1` (d) nothing can be said

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 analyze the given angle \(\theta = -1042^\circ\) and determine the value of \(n = \tan(\theta)\). Here are the steps:

### Step 1: Normalize the Angle
First, we need to find a coterminal angle for \(-1042^\circ\) that lies within the standard range of \(0^\circ\) to \(360^\circ\). We can do this by adding \(360^\circ\) repeatedly until we get a positive angle.

\[ -1042 + 3 \times 360 = -1042 + 1080 = 38^\circ \]

Thus, \(-1042^\circ\) is coterminal with \(38^\circ\).

### Step 2: Calculate \(\tan(\theta)\)
Now, we can find \(n = \tan(\theta)\) where \(\theta = 38^\circ\).

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

### Step 3: Determine the Value of \(\tan(38^\circ)\)
The tangent of \(38^\circ\) can be evaluated using a calculator or trigonometric tables.

\[ \tan(38^\circ) \approx 0.7813 \]

### Step 4: Compare \(n\) with 1
Now we need to compare \(n\) with 1.

Since \(0.7813 < 1\), we conclude that:

\[ n < 1 \]

### Step 5: Select the Correct Option
From the options provided:
(a) \(n > 1\)
(b) \(n < 1\)
(c) \(n = 1\)
(d) nothing can be said

The correct option is (b) \(n < 1\).

### Final Answer
The answer is (b) \(n < 1\).

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