SSC CGL 4 Sep 2016 Paper

⇒ 3 sin θ – 3 cos θ = sin θ + cos θ
⇒ 3 sin θ – sin θ = 3 cos θ + cos θ
⇒ 2 sin θ = 4 cos θ
⇒ sin θ = 2 cos θ
⇒ tan θ = 2
∴ $\mathit{s}\mathit{e}{\mathit{c}}^2$ θ = 1 + $\mathit{t}\mathit{a}{\mathit{n}}^2$ θ
= 1 + 4 = 5
∴ $\mathit{c}\mathit{o}{\mathit{s}}^2$ θ = $\frac{1}{5}$
∴ $\mathit{s}\mathit{i}{\mathit{n}}^2$ θ = 1 - $\mathit{c}\mathit{o}{\mathit{s}}^2$ θ
= 1 - $\frac{1}{5}$ = $\frac{4}{5}$
∴ $\mathit{s}\mathit{i}{\mathit{n}}^4\mathit{\theta }-\mathit{c}\mathit{o}{\mathit{s}}^4\mathit{\theta }$
= $\left(\mathit{s}\mathit{i}{\mathit{n}}^2\mathit{\theta }+\mathit{c}\mathit{o}{\mathit{s}}^2\mathit{\theta }\right)$ $\left(\mathit{s}\mathit{i}{\mathit{n}}^2\mathit{\theta }-\mathit{c}\mathit{o}{\mathit{s}}^2\mathit{\theta }\right)$
= 1 - $\frac{1}{5}$ = $\frac{4}{5}$
∴ $\mathit{s}\mathit{i}{\mathit{n}}^2\mathit{\theta }-\mathit{c}\mathit{o}{\mathit{s}}^2\mathit{\theta }$ = $\frac{4}{5}-\frac{1}{5}$ = $\frac{3}{5}$