Question

Evaluate the following expressions :
$4co{t}^2{45}^{\circ }-se{c}^2{60}^{\circ }+si{n}^2{60}^{\circ }+co{s}^2{90}^{\circ }$

Answer 1

We have,
$4co{t}^2{45}^{\circ }-se{c}^2{60}^{\circ }+si{n}^2{60}^{\circ }+co{s}^2{90}^{\circ }$
$=4(cot{45}^{\circ }{)}^2-(sec{60}^{\circ }{)}^2+(sin{60}^{\circ }{)}^2+(cos{90}^{\circ }{)}^2$
$=4\times (1{)}^2-(2{)}^2+{\left(\frac{\sqrt{3}}{2}\right)}^2+0=4-4+\frac{3}{4}+0=\frac{3}{4}$