Question

$co{t}^2{30}^{\circ }-2co{s}^2{30}^{\circ }-\frac{3}{4}se{c}^2{45}^{\circ }+\frac{1}{4}cose{c}^2{30}^{\circ }$

Answer 1

$co{t}^2{30}^{\circ }-2co{s}^2{30}^{\circ }-\frac{3}{4}se{c}^2{45}^{\circ }+\frac{1}{4}cose{c}^2{30}^{\circ }$

Putting values of the trigonometric values,

$co{t}^2{30}^{\circ }-2co{s}^2{30}^{\circ }-\frac{3}{4}se{c}^2{45}^{\circ }+\frac{1}{4}cose{c}^2{30}^{\circ }=(\sqrt{3}{)}^2-2(\frac{\sqrt{3}}{2}{)}^2-\frac{3}{4}(\sqrt{2}{)}^2-(2{)}^2$

$=3-\frac{3}{2}-\frac{3}{2}-1=3-3-1=-1$