Question

Which expression does sine of the quantity pi plus theta end quantity plus cosine of the quantity pi over 2 minus theta end quantity simplify to?

Answer 1

Step-by-step explanation:

The expression that we have is

`sin(\pi+\theta)+cos((\pi)/(2)-\theta)`

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

`sin(\pi+\theta)=-sin\theta`

Therefore, the expression now is:

`-s\imaginaryI n(\theta)+cos((\pi)/(2)-\theta)`

Step 2. Then we use the following cosine property to simplify the second term:

`cos((\pi)/(2)-\theta)=sin\theta`

Substituting this into our expression:

`-sin\theta+sin\theta`

Step 3. We have the same expression sine of theta with negative and positive signs and they cancel each other. The result is 0:

`-sin\theta+sin\theta=0`

Answer: 0