Question

Evalute,
$\cos {}^2\left(0\right)+\cos {}^2\left(\frac{\Pi }{6}\right)+\cos {}^2\left(\frac{\Pi }{3}\right)\cos {}^2\left(\frac{\Pi }{2}\right)$

Answer 1

${\cos }^2\left(0\right)+{\cos }^2\left(\frac{\pi }{6}\right)+{\cos }^2\left(\frac{\pi }{3}\right)+{\cos }^2\left(\frac{\pi }{2}\right)$

$\because \cos \frac{\pi }{2}=0,{\cos }^o=1$

& $\cos \frac{\pi }{6}=\frac{\sqrt{3}}{2},\cos \frac{\pi }{3}=\frac{1}{2}$

$\Rightarrow {\cos }^2\left(0\right)+{\cos }^2\left(\frac{\pi }{6}\right)+{\cos }^2\left(\frac{\pi }{3}\right){\cos }^2\left(\frac{\pi }{2}\right)$

$\Rightarrow 1+{\left(\frac{\sqrt{3}}{2}\right)}^2+{\left(\frac{1}{2}\right)}^2$

$\Rightarrow 1+\frac{3}{4}=\frac{7}{4}$