The value of $$2\tan \frac{\pi }{{10}} + 3\sec \frac{\pi }{{10}} - 4\cos \frac{\pi }{{10}}$$       is

Solution :
Value $$ = \frac{{2\sin {{18}^ \circ } + 3 - 4{{\cos }^2}{{18}^ \circ }}}{{\cos {{18}^ \circ }}} = \frac{{2\sin {{18}^ \circ } + 3 - 2\left( {1 + \cos {{36}^ \circ }} \right)}}{{\cos {{18}^ \circ }}}$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{2 \cdot \frac{{\sqrt 5 - 1}}{4} + 3 - 2 - 2 \cdot \frac{{\sqrt 5 + 1}}{4}}}{{\cos {{18}^ \circ }}} = 0.$$