Question

Show that $\frac{cos 15° + sin 15°}{cos 15° - sin 15°} =\sqrt{3}$

Answer 1

$LHS = \frac{ \cos(15°) + \sin(15°) }{ \cos(15°) - \sin(15°) }$

OR

$= \frac{cos15° + sin(90° - 75°)}{cos15° - sin(90° - 75°)}$

$= \frac{cos15 °+ cos75°}{cos15 °- cos75°}$

$= \frac{2cos45° \times cos ( - 30°)}{ - 2sin45° \times \sin( - 30°) }$

$= \frac{ - \cos(90° - 45°) \times \frac{ \sqrt{3} }{2} }{ \sin(45°) \times ( - \frac{1}{2} )}$

$= \frac{ - \sin(45°) \times \frac{ \sqrt{3} }{2} }{ \sin(45°) \times ( - \frac{1}{2} )}$

$= \frac{ - \frac{ \sqrt{3} }{2} }{ - \frac{1}{2} }$

$= \sqrt{3} = RHS$

Hence, proved