Question

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

• A. 1
• B. 2
• C. 3
• D. 0

Answer 1

Answer: (B)

2

Answer 2

$\frac{\frac{\sin 70^{o}}{\cos 70^{o}} - \frac{\sin 20^{o}}{\cos 20^{o}}}{\frac{\sin 50^{o}}{\cos 50^{o}}} = \frac{\frac{\sin 70^{o}\cos 20^{o} - \cos 70^{o}\sin 20^{o}}{\cos 70^{o}.\cos 20^{o}}}{\frac{\sin 50^{o}}{\cos 50^{o}}}$

= $\frac{2}{2} \times \frac{\sin(70^{o} - 20^{o})\cos 50^{o}}{\cos 70^{o}.\cos 20^{o}.\sin 50^{o}} = \frac{2\sin 50^{o}.\cos 50^{o}}{2\cos 70^{o}\cos 20^{o}.\sin 50^{o}}$

= $\frac{2\cos 50^{o}}{\cos 90^{o} + \cos 50^{o}} = \frac{2\cos 50^{o}}{0 + \cos 50^{o}} = 2$.