Question

True or False$\cos (\frac{\mathrm{\pi }}{2}-\theta )=\cos \theta$

Short answer

$\cos (\frac{\mathrm{\pi }}{2}-\theta )=\cos \theta$is false.

Step-by-step solution

Step 1. Given information 

Given that $\cos (\frac{\mathrm{\pi }}{2}-\theta )=\cos \theta$.

We have to tell whether this is true or false.

Step 2. Apply the difference of cosine function

We know $\cos (\alpha -\beta )=\cos \alpha \cos \beta +\sin \alpha \sin \beta$.

$$\begin{gathered} \cos (\frac{\mathrm{\pi }}{2}-\theta )=\cos \frac{\mathrm{\pi }}{2}\cos \theta +\sin \frac{\mathrm{\pi }}{2}\sin \theta \\ =0\cos \theta +1\sin \theta \\ =\sin \theta \end{gathered}$$

Therefore, $\cos (\frac{\mathrm{\pi }}{2}-\theta )=\cos \theta$is false.