For all $$\propto'_i{_s}, (i = 1, 2, 3, .........20)$$ lying between $$0^\circ  and  90^\circ$$, it is given that, $$\cos \propto_1 + \cos \propto_2 + \cos \propto_3 +.......... + \cos \propto_{20} = 20$$. What is the value of $$(\propto_1 + \propto_2 + \propto_3 + ......... + \propto_{20})$$ ?

$$\cos \propto_1 + \cos \propto_2 + \cos \propto_3 +.......... + \cos \propto_{20} = 20$$

As given that values will be between $$0^\circ and 90^\circ$$.

Here we know that $$cos 0^\circ = 1$$ and $$cos 90^\circ = 0$$

So the value of each of the $$\propto$$ will be $$0^\circ$$ for satisfying the above given equation.

The value of $$(\propto_1 + \propto_2 + \propto_3 + ......... + \propto_{20})$$ = 20 times of $$0^\circ$$ = 20$$\times\ 0^\circ$$

= $$0^\circ$$