Question

please help please..........?

Answer 1

Numerator:

⇒ sin 23θ - sin 7θ

We know that sinA - sinB = 2 cos(A + B)/2 sin(A - B)/2

⇒ 2 cos(23θ + 7θ)/2 sin(23θ - 7θ)/2

⇒ 2 cos 15θ sin 8θ

Denominator:

⇒ sin 2θ + sin 14θ

We know that sinA + sinB = 2 sin(A + B)/2 cos(A - B)/2

⇒ 2 sin8θ cos6θ

Now,

Numerator/Denominator:

⇒ (sin 23θ - sin 7θ)/(sin 2θ + sin 14θ)

⇒ (2 cos 15θ sin 8θ)/(2 sin 8θ cos 6θ)

⇒ (cos 15θ)/(cos 6θ).

Given : θ = π/21

⇒ cos(15 * π/21)/(cos 6 * π/21)

⇒ cos(5π/7)/cos(2π/7)

⇒ cos(5π)/cos(2π)

We know that cos(90 - θ) = sin θ.

⇒ sin(π/2 - 5π/7)/sin(π/2 - 2π/7)

⇒ sin(-3π/14)/sin(3π/14)

⇒ -sin(3π/14)/sin(3π/14)

⇒ -1.

Therefore, the answer is -1.

Hope it helps!

Answer 2

Answer is -1 to this question