Question

( sin pi/6 + cos pi/6.) (sin pi/3 - cos pi/3)​

Answer 1

Step-by-step explanation:

$( \sin \frac{\pi}{6} + \cos\frac{\pi}{6}).( \sin \frac{\pi}{3} - \cos\frac{\pi}{3}) \\ = ( \frac{1}{2} + \frac{ \sqrt{3} }{2} ).( \frac{ \sqrt{3} }{2} - \frac{1}{2}) \\ = ( { \frac{ \sqrt{3} }{2} })^{2} - ( { \frac{1}{2} })^{2} \\ = \frac{3}{4} - \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$