Question

Jika sin(2x+30°) = a dan cos(x+75°)=b ,maka cos(3x+105°) cos(x-45°) adlh ?

Answer 1

cos(3x+105) . cos(x - 45)
= 1/2[cos(3x+105 + x - 45) + cos (3x + 105 - x + 45)]
= 1/2[cos (4x + 60) + cos (2x + 150)]
= 1/2[cos 2(2x + 30) + cos 2(x + 75)]
= 1/2 [1 - 2sin²(2x+30) + 1 - 2sin²(x+75)]
= 1/2[2 - 2a² - 2b² ]
= 1 - a² - b²