2. Jika cos (x+30°) a dengan 0° ≤ x ≤ 360°. maka cos (2x +15°) adalah: ... SBMPTN 2015

cos (x + 30°) = a = a/1 = sa/mi => de = √(1^2 - a^2) = √(1 - a^2)
sin (x + 30°) = de/mi = √(1 - a^2)/1 = √(1 - a^2)

cos 2(x + 30°) = cos^2 (x + 30°) - sin^2 (x + 30°)
= (a)^2 - (√(1 - a^2))^2
= a^2 - (1 - a^2)
= 2a^2 - 1
sin 2(x + 30°) = 2 sin (x + 30°) cos (x + 30°)
= 2 √(1 - a^2) . a
= 2a√(1 - a^2)

cos (2x + 15°) = cos (2x + 60° - 45°)
= cos (2(x + 30°) - 45°)
= cos 2(x + 30°) cos 45° + sin 2(x + 30°) sin 45°
= (2a^2 - 1) . 1/2 √2 + 2a√(1 - a^2) . 1/2 √2
= 1/2 √2 (2a^2 - 1) + a√(2(1 - a^2))