Using exact values for standard angles, work out \(4\sin^2 60^\circ+3\tan^2 30^\circ-8\sin 45^\circ\cos 45^\circ\).
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 0
Put in the standard values \(\sin 60^\circ=\frac{\sqrt{3}}{2}\), \(\tan 30^\circ=\frac{1}{\sqrt{3}}\) and \(\sin 45^\circ=\cos 45^\circ=\frac{1}{\sqrt{2}}\).
\(4\sin^2 60^\circ=4\times\displaystyle\frac{3}{4}=3\)
\(3\tan^2 30^\circ=3\times\displaystyle\frac{1}{3}=1\)
\(8\sin 45^\circ\cos 45^\circ=8\times\displaystyle\frac{1}{\sqrt{2}}\times\frac{1}{\sqrt{2}}=4\)
Value \(=3+1-4=0\)