Question

Evaluate the following expressions :
$cose{c}^2{30}^{\circ }si{n}^2{45}^{\circ }-se{c}^2{60}^{\circ }$

Answer 1

We have,
$cose{c}^2{30}^{\circ }si{n}^2{45}^{\circ }-se{c}^2{60}^{\circ }$
$=\left(cosec{30}^{\circ }{)}^2\right(sin{45}^{\circ }{)}^2-(sec{60}^{\circ }{)}^2=(2{)}^2\times {\left(\frac{1}{\sqrt{2}}\right)}^2-(2{)}^2=2-4=-2$