What does \(2\,\mathrm{cosec}^2 30^\circ+3\sec^2 45^\circ-4\cot^2 60^\circ\) simplify to?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\displaystyle\frac{38}{3}\)
Use the standard values \(\mathrm{cosec}\,30^\circ=2\), \(\sec 45^\circ=\sqrt{2}\) and \(\cot 60^\circ=\frac{1}{\sqrt{3}}\), and square each one.
\(2\,\mathrm{cosec}^2 30^\circ=2\times 4=8\)
\(3\sec^2 45^\circ=3\times 2=6\)
\(4\cot^2 60^\circ=4\times\displaystyle\frac{1}{3}=\frac{4}{3}\)
Value \(=8+6-\displaystyle\frac{4}{3}=\frac{42-4}{3}=\frac{38}{3}\)