SSC CGL 2025 PYQ — Question 57

The correct answer is option 1 i.e. $\frac{\sqrt{2}}{2}$.

$\sin A + \cos A = \sqrt{2}$

⇒ $(\sin A + \cos A)^2 = (\sqrt{2})^2=2$

⇒ $\sin^2 A + \cos^2 A + 2\sin A \cos A = 2$

⇒ 2 sin A cos A = 1

⇒ sin A cos A = 1/2

$\sin^3 A + \cos^3 A = (\sin A + \cos A)(\sin^2 A - \sin A\cos A + \cos^2 A)$

$= (\sin A + \cos A) \left[ (\sin^2 A + \cos^2 A) - \sin A\cos A \right]$

$= \sqrt{2} \times \left(1 - \frac12\right)$

$= \sqrt{2} \times \frac12$

$= \frac{\sqrt{2}}{2}$