Question

Hi please help me with this math question​

Answer 1

Step-by-step explanation:

cos(3x) = sin(2x)

Use reflection.

sin(π/2 − 3x) = sin(2x)

π/2 − 3x = 2x

π/2 = 5x

x = π/10

Instead, use multiple angle formulas.

cos(3x) = sin(2x)

4 cos³x − 3 cos x = 2 sin x cos x

4 cos³x − 3 cos x − 2 sin x cos x = 0

cos x (4 cos²x − 3 − 2 sin x) = 0

cos x (4 (1 − sin²x) − 3 − 2 sin x) = 0

cos x (4 − 4 sin²x − 3 − 2 sin x) = 0

-cos x (-4 + 4 sin²x + 3 + 2 sin x) = 0

-cos x (4 sin²x + 2 sin x − 1) = 0

If t = sin(π/10), then:

4t² + 2t − 1 = 0

Solve with quadratic formula:

t = [ -2 ± √(2² − 4(4)(-1)) ] / 2(4)

t = [ -2 ± √(4 + 16) ] / 8

t = (-2 ± 2√5) / 8

t = (-1 ± √5) / 4

Since π/10 is in the first quadrant, sin(π/10) is positive.

sin(π/10) = (-1 + √5) / 4