`"cosec" (90^(@)- theta)=?`

Options

A. ` tan theta`
B. `cot theta`
C. `sec theta`
D. `cos theta`

Answer

To solve the problem \( \csc(90^\circ - \theta) \), we can use the co-function identity of trigonometric functions. Here’s a step-by-step solution:

### Step 1: Understand the Co-Function Identity
The co-function identity states that:
\[ \csc(90^\circ - \theta) = \sec(\theta) \]
This means that the cosecant of an angle minus 90 degrees is equal to the secant of the angle.

### Step 2: Apply the Co-Function Identity
Using the identity from Step 1, we can directly substitute:
\[ \csc(90^\circ - \theta) = \sec(\theta) \]

### Step 3: Identify the Correct Option
Now, let's look at the options provided:
1. \( 7 \)
2. \( 10\theta \)
3. \( \cot\theta \)
4. \( \sec\theta \)
5. \( \csc\theta \)

From our calculation, we found that \( \csc(90^\circ - \theta) = \sec(\theta) \). Therefore, the correct answer is:
\[ \sec\theta \]

### Final Answer
Thus, the answer to the question \( \csc(90^\circ - \theta) \) is:
\[ \sec\theta \]

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