SSC CPO SI and ASI Model Paper 4

(2)$\mathit{c}\mathit{o}{\mathit{s}}^{21}°+\mathit{c}\mathit{o}{\mathit{s}}^{25}°+\mathit{c}\mathit{o}{\mathit{s}}^{29}°+\dots +\mathit{c}\mathit{o}{\mathit{s}}^{285}°+\mathit{c}\mathit{o}{\mathit{s}}^{289}°$
In the given expression we can seethat the angles are 1° , 5° , 9° , 13° ,…, 81° , 85° , 89°
Let the number of terms in theexpression be n.
$\therefore \mathit{a}+\left(\mathit{n}\mathit{–}1\right)\mathit{d}={\mathit{t}}_{\mathit{n}}$
⇒ 1 + (n – 1)4 = 89
⇒ n = 23
$\therefore \mathit{c}\mathit{o}{\mathit{s}}^{21}°+\mathit{c}\mathit{o}{\mathit{s}}^{25}°+\mathit{c}\mathit{o}{\mathit{s}}^{29}°+\dots +\mathit{c}\mathit{o}{\mathit{s}}^{285}°+\mathit{c}\mathit{o}{\mathit{s}}^{289}$°
$=\mathit{c}\mathit{o}{\mathit{s}}^{21}°+\mathit{c}\mathit{o}{\mathit{s}}^{289}°+\mathit{c}\mathit{o}{\mathit{s}}^{25}°+\mathit{c}\mathit{o}{\mathit{s}}^{285}°+\dots +\mathit{c}\mathit{o}{\mathit{s}}^{237}°+\mathit{c}\mathit{o}{\mathit{s}}^{253}°+\mathit{c}\mathit{o}{\mathit{s}}^{241}°+\mathit{c}\mathit{o}{\mathit{s}}^{249}°+\mathit{c}\mathit{o}{\mathit{s}}^{245}°$
$=\mathit{c}\mathit{o}{\mathit{s}}^{21}°+\mathit{s}\mathit{i}{\mathit{n}}^{21}°+\mathit{c}\mathit{o}{\mathit{s}}^{25}°+\mathit{s}\mathit{i}{\mathit{n}}^{25}°+\dots +\mathit{c}\mathit{o}{\mathit{s}}^{241}°+\mathit{s}\mathit{i}{\mathit{n}}^{241}°+\mathit{c}\mathit{o}{\mathit{s}}^{245}°$
$={\left[1+1+1+\dots +1\right]}_{\left(11\mathit{t}\mathit{i}\mathit{m}\mathit{e}\mathit{s}\right)}+{\left(\frac{1}{\sqrt{2}}\right)}^2$
$=\frac{23}{2}$