Question

cot²30° − 2cos²30° − $\frac{3}{4}$ sec²45° + $\frac{1}{4}$ cosec²30°

Answer 1

On substituting the values of various T-ratios, we get:
cot² 30^o − 2 cos² 30^o − $\frac{3}{4}$ sec² 45^o + $\frac{1}{4}$ cosec² 30^o
$$\begin{gathered} ={\left(\sqrt{3}\right)}^2-2\times {\left(\frac{\sqrt{3}}{2}\right)}^2-\frac{3}{4}\times {\left(\sqrt{2}\right)}^2+\frac{1}{4}\times {\left(2\right)}^2 \\ =3-2\times \frac{3}{4}-\frac{3}{4}\times 2+\frac{1}{4}\times 4 \\ =3-\frac{3}{2}-\frac{3}{2}+1 \\ =4-\left(\frac{3}{2}+\frac{3}{2}\right) \\ =4-3 \\ =1 \end{gathered}$$