Question

If ${\sin }^2{\theta }_1+{\sin }^2{\theta }_2+...+{\sin }^2{\theta }_n=0$ then find the minimum value of ${\cos }^2{\theta }_1+{\cos }^2{\theta }_2+...+{\cos }^2{\theta }_n$

Answer 1

Given, ${\sin }^2{\theta }_1+{\sin }^2{\theta }_2+...+{\sin }^2{\theta }_n=0$

$\Rightarrow {\theta }_1,{\theta }_2...{\theta }_n=0$

$\therefore {\cos }^2{\theta }_1,{\cos }^2{\theta }_2,...{\cos }^2{\theta }_n=1$

$\Rightarrow {\cos }^2{\theta }_1+{\cos }^2{\theta }_2+...+{\cos }^2{\theta }_n=n$