What is the value of (`1/3` - cosec`30^@`)?

Options

A. `(sqrt6-1)/sqrt3`
B. `-1/2`
C. `-5/3`
D. `3/2`

Answer

To solve the question, "What is the value of (1/3 - cosec 30°)?", we can follow these steps:

### Step 1: Understand the cosecant function
The cosecant function is the reciprocal of the sine function. Therefore, cosec(θ) = 1/sin(θ).

### Step 2: Find the value of cosec 30°
We know that sin(30°) = 1/2. Thus, cosec(30°) = 1/sin(30°) = 1/(1/2) = 2.

### Step 3: Substitute the value of cosec 30° into the expression
Now we can substitute this value back into the expression:
1/3 - cosec(30°) = 1/3 - 2.

### Step 4: Convert to a common denominator
To subtract these fractions, we need a common denominator. The least common multiple of 3 and 1 is 3. We can express 2 as a fraction with a denominator of 3:
2 = 2/1 = 6/3.

### Step 5: Perform the subtraction
Now we can perform the subtraction:
1/3 - 6/3 = (1 - 6)/3 = -5/3.

### Final Answer
The value of (1/3 - cosec 30°) is -5/3.

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