Question

True or False:$\sin \left(-\theta \right)+\cos \left(-\theta \right)=\cos \left(\theta \right)-\sin \left(\theta \right)$

Short answer

The given identity is true

Step-by-step solution

Given information

We are given a identity$\sin \left(-\theta \right)+\cos \left(-\theta \right)=\cos \left(\theta \right)-\sin \left(\theta \right)$

Explanation for true statement

We know that,

$$\begin{gathered} \sin \left(-\theta \right)=-\sin \left(\theta \right) \\ \cos \left(-\theta \right)=\cos \left(\theta \right) \end{gathered}$$

On adding these two we get,

$$\begin{gathered} \sin \left(-\theta \right)+\cos \left(-\theta \right) \\ =\cos \left(\theta \right)-\sin \left(\theta \right) \end{gathered}$$

Hence the given statement is true statement

Conclusion

The given identity is true