# How do you verify the identity cos^2beta+cos^2(pi/2-beta)=1?

Jan 16, 2017

See the proof below

#### Explanation:

$\cos \left(\frac{\pi}{2}\right) = 0$

$\sin \left(\frac{\pi}{2}\right) = 1$

$\cos \left(\frac{\pi}{2} - \beta\right) = \cos \left(\frac{\pi}{2}\right) \cos \beta + \sin \left(\frac{\pi}{2}\right) \sin \beta$

$= 0 + \sin \beta$

Therefore,

$L H S = {\cos}^{2} \beta + {\cos}^{2} \left(\left(\frac{\pi}{2}\right) - \beta\right)$

$= {\cos}^{2} \beta + {\sin}^{2} \beta = 1 = R H S$

$Q E D$