Question

The value of $\frac{\tan 70^{\circ }-\tan 20^{\circ }}{\tan 50^{\circ }}=$

• A. 1
• B. 2
• C. 3
• D. 0

Answer 1

Answer: (B)

$\frac{\tan 70^{\circ }-\tan 20^{\circ }}{\tan 50^{\circ }}=\frac{\frac{\sin 70^{\circ }}{\cos 70^{\circ }}-\frac{\sin 20^{\circ }}{\cos 20^{\circ }}}{\frac{\sin 50^{\circ }}{\cos 50^{\circ }}}$
$\frac{\frac{sin70^{\circ }cos20^{\circ }-cos70^{\circ }sin20^{\circ }}{cos70^{\circ }cos20^{\circ }}}{\frac{sin50^{\circ }}{cos50^{\circ }}}$
$=\frac{2}{2}\times \frac{\sin \left(70^{\circ }-20^{\circ }\right)\cos 50^{\circ }}{\cos 70^{\circ }\cos 20^{\circ }\sin 50^{\circ }}=\frac{2\sin 50^{\circ }\cos 50^{\circ }}{2\cos 70^{\circ }\cos 20^{\circ }\sin 50^{\circ }}$
$=\frac{2\cos 50^{\circ }}{\cos 90^{\circ }+\cos 50^{\circ }}=\frac{2\cos 50^{\circ }}{0+\cos 50^{\circ }}=2$