Question

Tunjukkan bahwa:
a. sin⁡〖75°〗= 1/4 √2 (1+√3)
b. sin⁡〖345°〗= 1/2 √2 (1-√3)

Answer 1

Sin 75 = sin (45 + 30) = sin 45 cos 30 + cos 45 sin 30
= ½√ 2 .  ½√ 3 +  ½√ 2 . ½ 
=½√ 2 (½√ 3 + ½)
=  ¼√ 2 (√ 3 +1)
= ¼√ 2 (1+√ 3)
,
sin 345 = sin (360-15) = - sin 15
- sin 15 = - sin(45 - 30)= - [ sin 45 cos 30 - cos 30 sin 45 ]
- sin 15 = - [½√ 2 .  ½√ 3 -  ½√ 2 . ½ 
- sin 45 = - [½√ 2 (½√ 3- ½)]
- sin 45 = - [¼√ 2 (√ 3 -1)]
- sin 45 = ¼√ 2 (1-√ 3)
sin 345  =¼√ 2 (1-√ 3)