Find `sin (90^(@)- theta)`
A. `cos 90^(@)`
B. `1//2`
C. 1
D. `cos theta`

Options

A. B
B. C
C. A
D. D

Answer

To solve the problem of finding \( \sin(90^\circ - \theta) \), we can use the sine subtraction identity. Here’s the step-by-step solution:

### Step 1: Understand the Sine Identity
We know from trigonometric identities that:
\[ \sin(90^\circ - \theta) = \cos(\theta) \]
This is a fundamental identity in trigonometry.

### Step 2: Apply the Identity
Using the identity directly:
\[ \sin(90^\circ - \theta) = \cos(\theta) \]

### Step 3: Verify the Options
Now, let's compare this result with the provided options:
- A. \( \cos(90^\circ) \) (which equals 0)
- B. \( \frac{1}{2} \)
- C. 1
- D. \( \cos(\theta) \)

Since we found that \( \sin(90^\circ - \theta) = \cos(\theta) \), the correct answer is:
\[ \text{Option D: } \cos(\theta) \]

### Final Answer
Thus, the answer is \( \cos(\theta) \).

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