The diagram below shows an isosceles triangle $ABC$, where $AB = AC = 2$ cm, and a square \

Question

The diagram below shows an isosceles triangle $ABC$, where $AB = AC = 2$ cm, and a square $BCDE$. $M$ is the midpoint of $BC$. Angle $BAM = \theta$ and can vary. Show that the total area of $ABEDC$ is $16 \sin^2 \theta + 4 \sin \theta \cos \theta$ cm$^{2}$.[3] Show that $16 \sin^2 \theta + 4 \sin \theta \cos \theta = 2 \sin 2\theta - 8 \cos 2\theta + 8$.[2] Express $2\sin2\theta-8\cos2\theta$ in the form $R\sin(2\theta-\alpha)$, where $R > 0 $ and $0^\circ <$ $\alpha < 90^\circ$[3]

Accepted Answer

(c)$\sqrt{68}\sin (2\theta-76.0^\circ)$

2025 DSS PRELIMS P2 Q6

2025 DSS PRELIMS P2 Q6