MATH SOLVE

3 months ago

Q:
# plsss help...i need someone to help with my hw..cuz my teacher wants them to be done by tomorrow. .

Accepted Solution

A:

Step-by-step explanation:(1)sin(3θ) = sin(2θ)Double and triple angle formulas:3 sin θ − 4 sin³ θ = 2 sin θ cos θsin θ ≠ 0, so divide both sides by sin θ:3 − 4 sin² θ = 2 cos θPythagorean identity:3 − 4 (1 − cos² θ) = 2 cos θ3 − 4 + 4 cos² θ = 2 cos θ4 cos² θ − 2 cos θ − 1 = 0Quadratic formula:cos θ = [ 2 ± √((-2)² − 4(4)(-1)) ] / 2(4)cos θ = (2 ± √20) / 8cos θ = (2 ± 2√5) / 8cos θ = (1 ± √5) / 4θ = 36°, so it's in the first quadrant. Therefore, cos θ > 0.cos θ = (1 + √5) / 4(2)sin³(2x) cos(6x) + cos³(2x) sin(6x)Multiply and divide by 4:¼ (4 sin³(2x) cos(6x) + 4 cos³(2x) sin(6x))Power reduction formula:¼ ((3 sin(2x) − sin(6x)) cos(6x) + (3 cos(2x) + cos(6x)) sin(6x))¼ (3 sin(2x) cos(6x) − sin(6x) cos(6x) + 3 cos(2x) sin(6x) + cos(6x) sin(6x))¼ (3 sin(2x) cos(6x) + 3 cos(2x) sin(6x))¾ (sin(2x) cos(6x) + cos(2x) sin(6x))Angle sum formula:¾ sin(8x)