Question

Find the value of ${\csc }^2{30}^o-{\sin }^2{45}^o-{\sec }^2{60}^o$

Answer 1

Using trigonometric table,

$\csc 30°=2$

$\sin 45°=\frac{1}{\sqrt{2}}$

$\sec 60°=2$

Therefore,

${\csc }^{2}30°-{\sin }^{2}45°-{\sec }^{2}60°$

$={\left(2\right)}^2-{\left(\frac{1}{\sqrt{2}}\right)}^2-{\left(2\right)}^2$

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