Plsss need someone to with my hw..cuz my teacher wants them to be done by tomorrow.

Step-by-step explanation:

(1)

sin(3θ) = sin(2θ)

Double and triple angle formulas:

3 sin θ − 4 sin³ θ = 2 sin θ cos θ

sin θ ≠ 0, so divide both sides by sin θ:

3 − 4 sin² θ = 2 cos θ

Pythagorean identity:

3 − 4 (1 − cos² θ) = 2 cos θ

3 − 4 + 4 cos² θ = 2 cos θ

4 cos² θ − 2 cos θ − 1 = 0

Quadratic formula:

cos θ = [ 2 ± √((-2)² − 4(4)(-1)) ] / 2(4)

cos θ = (2 ± √20) / 8

cos θ = (2 ± 2√5) / 8

cos θ = (1 ± √5) / 4

θ = 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)

3/4 ÷ 3/4

step-by-step explanation:

basically divide any proper fraction with itself to fit the criteria.

so if we are using 3/4, then:

3/4 ÷ 3/4 = 1

so 1 is the quotient.

and the numerators for both these fractions is 3.   and if we divide the numerators:

3 ÷ 3 = 1

we see that quotient is equal to our original quotient as well.

-4

step-by-step explanation: