Question
The value of $$\tan {20^ \circ } + 2\tan {50^ \circ } - \tan {70^ \circ }$$ is
A.
$$1$$
B.
$$0$$
C.
$$\tan {50^ \circ }$$
D.
None of these
Answer :
$$0$$
Solution :
Value $$ = 2\tan {50^ \circ } - \left( {\tan {{70}^ \circ } - \tan {{20}^ \circ }} \right)$$
$$\eqalign{
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 2\tan {50^ \circ } - \frac{{\sin {{50}^ \circ }}}{{\cos {{70}^ \circ } \cdot \cos {{20}^ \circ }}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 2\tan {50^ \circ } - \frac{{2\sin {{50}^ \circ }}}{{2\sin {{20}^ \circ } \cdot \cos {{20}^ \circ }}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 2\tan {50^ \circ } - 2 \cdot \frac{{\sin {{50}^ \circ }}}{{\sin {{40}^ \circ }}} = 2\tan {50^ \circ } - 2 \cdot \frac{{\sin {{50}^ \circ }}}{{\cos {{50}^ \circ }}} = 0. \cr} $$