tolong dibantu soal matematika sbmptn nih

Kelas 11 Matematika
Bab Trigonometri Lanjut

sin x + cos x = a
(sin x + cos x)² = a²
(sin² x + 2 sin x cos x + cos² x) = a²
(sin² x + cos² x + 2 sin x cos x) = a²
1 + sin 2x = a²
sin 2x = a² - 1

tan 2x = 3/4 → y/x

r = √(x² + y²)
r = √(3² + 4²)
r = √(9 + 16)
r = √25
r = 5

sin 2x = y/r
sin 2x = 3/5

sin 2x = sin 2x
a² - 1 = 3/5
a² = 1 + 3/5
a² = 5/5 + 3/5
a = √(8/5)
a = 2 √(2/5)
a = 2 . √2 / √5
a = (2/5) √10