Question

Hi can anyone help me with this ..​

Answer 1

Answer:

n = π/6, π/4, 3π/4, 5π/6

Step-by-step explanation:

sin(3n) − sin n = cos(2n)

Use double and triple angle formulas:

(3 sin n − 4 sin³ n) − sin n = 1 − 2 sin² n

2 sin n − 4 sin³ n = 1 − 2 sin² n

4 sin³ n − 2 sin² n − 2 sin n + 1 = 0

Factor by grouping:

2 sin² n (2 sin n − 1) − (2 sin n − 1) = 0

(2 sin² n − 1) (2 sin n − 1) = 0

Solve:

2 sin² n − 1 = 0

2 sin² n = 1

sin² n = 1/2

sin n = √2/2

n = π/4, 3π/4

2 sin n − 1 = 0

2 sin n = 1

sin n = 1/2

n = π/6, 5π/6