SSC CGL 19 Oct 2014 Shift 2 Paper

${\left(\mathit{s}\mathit{i}\mathit{n}\mathit{\alpha }+\mathit{c}\mathit{o}\mathit{s}\mathit{e}\mathit{c}\mathit{\alpha }\right)}^2$ + ${\left(\mathit{c}\mathit{o}\mathit{s}\mathit{\alpha }+\mathit{s}\mathit{e}\mathit{c}\mathit{\alpha }\right)}^2$ = k + $\mathit{t}\mathit{a}{\mathit{n}}^2$ α + $\mathit{c}\mathit{o}{\mathit{t}}^2$ α
⇒ $\mathit{s}\mathit{i}{\mathit{n}}^2$ α + $\mathit{c}\mathit{o}\mathit{s}\mathit{e}{\mathit{c}}^2$ α + 2 sin α . cosec α + $\mathit{c}\mathit{o}{\mathit{s}}^2$ α + $\mathit{s}\mathit{e}{\mathit{c}}^2$ α + 2 cos α .sec α = k + $\mathit{t}\mathit{a}{\mathit{n}}^2$ α + $\mathit{c}\mathit{o}{\mathit{t}}^2$ α
⇒ $\mathit{s}\mathit{i}{\mathit{n}}^2$ α + $\mathit{c}\mathit{o}{\mathit{s}}^2$ α + 2 + $\mathit{c}\mathit{o}\mathit{s}\mathit{e}{\mathit{c}}^2$ α + $\mathit{s}\mathit{e}{\mathit{c}}^2$ α + 2 = k + $\mathit{t}\mathit{a}{\mathit{n}}^2$ α + $\mathit{c}\mathit{o}{\mathit{t}}^2$ α
⇒ 5 + $\mathit{c}\mathit{o}\mathit{s}\mathit{e}{\mathit{c}}^2$ α + $\mathit{s}\mathit{e}{\mathit{c}}^2$ α = k + $\mathit{t}\mathit{a}{\mathit{n}}^2$ α + $\mathit{c}\mathit{o}{\mathit{t}}^2$ α
⇒ 5 + 1 + $\mathit{c}\mathit{o}{\mathit{t}}^2$ α + 1 + $\mathit{t}\mathit{a}{\mathit{n}}^2$ α = k + $\mathit{t}\mathit{a}{\mathit{n}}^2$ α + $\mathit{c}\mathit{o}{\mathit{t}}^2$ α
⇒ 7 + $\mathit{c}\mathit{o}{\mathit{t}}^2$ α + $\mathit{t}\mathit{a}{\mathit{n}}^2$ α = k + $\mathit{t}\mathit{a}{\mathit{n}}^2$ α + $\mathit{c}\mathit{o}{\mathit{t}}^2$ α
⇒ k = 7