Explanation:
The expression that we have is
[tex]sin(\pi+\theta)+cos(\frac{\pi}{2}-\theta)[/tex]
And we need to simplify and find the result.
Step 1. First, we use the following property of the sine to simplify the first term
[tex]sin(\pi+\theta)=-sin\theta[/tex]
Therefore, the expression now is:
[tex]-s\imaginaryI n(\theta)+cos(\frac{\pi}{2}-\theta)[/tex]
Step 2. Then we use the following cosine property to simplify the second term:
[tex]cos(\frac{\pi}{2}-\theta)=sin\theta[/tex]
Substituting this into our expression:
[tex]-sin\theta+sin\theta[/tex]
Step 3. We have the same expression sine of theta with negative and positive signs and they cancel each other. The result is 0:
[tex]-sin\theta+sin\theta=0[/tex]
Answer: 0
