tolong dijawab pertanyaan nya tentang relasi sudut

Trigonometri

1) sin 150 = sin (180-30)= sin 30 = 1/2
cos 300 = cos (360-60) = cos 60 = 1/2
tan 225 = tan (180+45) = tan 45 = 1
sin 300 = sin (360-60) = - sin 60 = - ¹/₂√3

(sin 150 + cos 300) / (tan 45 - sin 300) =
= (1/2 + 1/2) /(1 - 1/2√3)
= 1/ ( 1 - 1/2 √3)
= 2/(2 -√3)
= 2(2+√3)/ (4-3) = 2(2+√3)
= 4 + 2√3

2.  cos (A+B) = cos A cos B - sin A sin B
(A+B) = 30 dan cos A cos B = 3/4
cos 30 = 3/4 - sin A sin B
sin A sin B = 3/4 - cos 30 = 3/4 - 1/2 √3

cos (A-B) = cos A cos B + sin A sin B
cos (A-B) = 3/4 + 3/4  - 1/2 √3 =  3/2 - 1/2 √3
cos (A-B) = 1/2 ( 3 - √3)

3. sin 15 cos 165 - sin 165 cos 15 =
= cos 165 sin 15 - sin 165 cos 15
= - (sin 165 cos 15 - cos 165 sin 15)
= - { sin (165 - 15)}
= - {sin 150} = - { sin (180-30)}
= - sin 30
= - 1/2

4. 
2 sin A cos A =  sin 2A
(cos A+sin A)(cos A-sin A) = cos 2A

{ 2 sin 22¹/₂  cos 22¹/₂) / (cos 15 + sin 15)(cos 15-sin 15)=
=  { sin 2 (22¹/₂) } / {cos 2 (15)}
= sin 45/ cos 30
= (1/2 √2 ) / (1/2 √3)
= √2/√3
= ¹/₃ √6