Question

Cat face sin 75° - sin 15° ? Va rog frumos

Answer 1

Folosim formula sina-sinb=2sin[(a-b)/2]*cos[(a+b)/2]
=> 2sin[(75°-15°)/2]*cos[(75°+15°)/2]=
2sin30°*cos45°=2*(1/2)*(√2/2)=√2/2

Answer 2

sin 15°= sin (45° - 30°) = 
sin45°× cos30° - cos45° × sin30° =
1/√2 × √3/2 - 1/√2 × 1/2 =
√3/2√2 - 1/2√2 = 
 (√3 - 1)/2√2 

sin 75° = sin (45° + 30°) =
sin45°× cos30° + cos45°× sin30° =
1/√2 × √3/2  +  1/√2 × 1/2 = 
√3/2√2 + 1/2√2 = 
(√3+1)/2√2 


sin 75° -  sin 15°  =
(√3+1)/2√2  - (√3-1)/2√2 =
(√3+1-√3+1)/2√2  = 
2/2√2 = 
1/√2 = √2/2 ( in cazul rationalizarii)