Question

Evaluate:

${\cot }^2{30}^o-2{\cos }^2{60}^o-\frac{3}{4}{\sec }^2{45}^o-{\sin }^2{30}^o$.

Answer 1

Now,

${\cot }^2{30}^o-2{\cos }^2{60}^o-\frac{3}{4}{\sec }^2{45}^o-{\sin }^2{30}^o$

$=(\sqrt{3}{)}^2-2\times \frac{1}{2^2}-\frac{3}{4}\times (\sqrt{2}{)}^2-\frac{1}{2^2}$

$=3-\frac{1}{2}-\frac{3}{2}-\frac{1}{4}$

$=3-2-\frac{1}{4}$

$=1-\frac{1}{4}$

$=\frac{3}{4}$.