Question

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

Answer 1

We have,
$tan{60}^{\circ }cose{c}^2{45}^{\circ }+se{c}^2{60}^{\circ }tan{45}^{\circ }$

$=tan{60}^{\circ }(cosec{45}^{\circ }{)}^2+(sec{60}^{\circ }{)}^{2}tan{45}^{\circ }$

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