SSC CGL 2024 PYQ — Question 55

The correct answer is option 1 i.e. −1.

Given, $\bigg[{{ 4cos(90-θ)sin^3(90+θ)-4sin(90+θ)cos^3(90-θ) }\over {cos({180+8θ\over2})}} \bigg]$

⇒ $\bigg[{{ 4sinθ cos^3θ-4cosθsin^3θ}\over {cos({90+4θ})}} \bigg]$

⇒ $\bigg[{{ 4sinθ cosθ(cos^2θ - sin^2θ)}\over {-sin(4θ)}} \bigg]$

⇒ $\bigg[{{2(2sinθ cosθ)(cos2θ)}\over {-sin(4θ)}} \bigg]$

⇒ $\bigg[{{2(sin2θ)(cos2θ)}\over {-sin(4θ)}} \bigg]$

⇒ $\bigg[{{sin4θ}\over {-sin4θ}} \bigg]$ = -1