1. ## Verify trig identity

verify the identity.

cos(pi-theta) + sin(pi/2 + theta) = 0

2. Hello, overduex!

One method is to use the Compound-angle Formulas:

. . $\sin(A + B) \;=\;\sin(A)\cos(B) + \sin(B)\cos(A)$

. . $\cos(A - B) \;=\;\cos(A)\cos(B) + \sin(A)\sin(B)$

Verify the identity: . $
\cos(\pi-\theta) + \sin\left(\frac{\pi}{2} + \theta\right) \;= \;0$

Using the two formulas, we have:

. . ,. . $\cos(\pi)\cos\theta + \sin(\pi)\sin\theta + \sin\frac{\pi}{2}\cos\theta + \sin\theta\cos\frac{\pi}{2}$

. . $= \;\;-1\cdot\cos\theta + 0\cdot\sin\theta + 1\cdot\cos\theta + \sin\theta\cdot0 \;\;=\;\;-\cos\theta + 0 + \cos\theta + 0 \;=\;0$