Verify trig identity

**overduex** · November 25th 2007, 12:41 PM

verify the identity.

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

can anyone please explain... Thanks!!!

**Soroban** · November 25th 2007, 01:12 PM

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: . $<br /> \cos(\pi-\theta) + \sin\left(\frac{\pi}{2} + \theta\right) \;= \;0$

Using the two formulas, we have:

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

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

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