Let `l= sin theta, m=cos theta and n=tan theta`.
Q. If `theta=7` radian, then : (a)`l+m gt 0` (b) `l+m lt 0` (c) `l+m=0` (d) nothing can be said

Options

A. `l+m gt 0`
B. `l+m lt 0`
C. `l+m=0`
D. nothing can be said

Answer

To solve the problem step by step, we will analyze the given information and perform the necessary calculations.

### Step 1: Define the Variables
We are given:
- \( l = \sin \theta \)
- \( m = \cos \theta \)
- \( n = \tan \theta \)

### Step 2: Substitute the Value of \( \theta \)
We know that \( \theta = 7 \) radians. We need to find \( l + m \).

### Step 3: Calculate \( l + m \)
To find \( l + m \), we need to calculate \( \sin(7) + \cos(7) \).

### Step 4: Determine the Values of \( \sin(7) \) and \( \cos(7) \)
Using a calculator or trigonometric tables:
- \( \sin(7) \approx 0.65699 \)
- \( \cos(7) \approx 0.75390 \)

### Step 5: Add the Values
Now, we can add these values:
\[ l + m = \sin(7) + \cos(7) \approx 0.65699 + 0.75390 \approx 1.41089 \]

### Step 6: Analyze the Result
Since \( l + m \approx 1.41089 \), which is greater than 0, we conclude that:
\[ l + m > 0 \]

### Step 7: Choose the Correct Option
From the options provided:
(a) \( l + m > 0 \)
(b) \( l + m < 0 \)
(c) \( l + m = 0 \)
(d) Nothing can be said

The correct answer is option (a): \( l + m > 0 \).

### Final Answer
The answer is (a) \( l + m > 0 \).

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