jika sin{2x+30drajat}=a dan sin{x + 45drajat}=b,maka sin{3x+75drajat}sin{x-15drajat} a.{a-b}2 b.a2-b2 c.a2/akar2-b2/akar3 d.a2-2b/akar6+b2 e.2ab-1/akar6 mohon b

Rumus : cos 2x = 1 - 2 sin^2 x

sin (2x + 30°) = a
cos 2(2x + 30°) = 1 - 2 sin^2 (2x + 30°)
cos (4x + 60°) = 1 - 2a^2

sin (x + 45°) = b
cos 2(x + 45°) = 1 - 2 sin^2 (x + 45°)
cos (2x + 90°) = 1 - 2b^2

Rumus : -2 sin A sin B = cos (A + B) - cos (A - B)
sin A sin B = -1/2 (cos (A + B) - cos (A - B))
sin (3x + 75°) sin (x - 15°)
= -1/2 (cos ((3x + 75°) + (x - 15°)) - cos ((3x + 75°) - (x - 15°))
= -1/2 (cos (4x + 60°) - cos (2x + 90°))
= -1/2 ((1 - 2a^2) - (1 - 2b^2))
= -1/2 (-2a^2 + 2b^2)
= a^2 - b^2

^ = pangkat