Question

Solution of. sin 18​

Answer 1

Answer:

sin 18° = sin A = −1±5√4

Step-by-step explanation:

Let A = 18°                          

- Therefore, 5A = 90°

2A + 3A = 90˚

2θ = 90˚ - 3A

- Taking sine on both sides, we get

sin 2A = sin (90˚ - 3A) = cos 3A

2 sin A cos A = 4 cos^3 A - 3 cos A

2 sin A cos A - 4 cos^3A + 3 cos A = 0

cos A (2 sin A - 4 cos^2 A + 3) = 0

- Dividing both sides by cos A = cos 18˚ ≠ 0, we get

2 sin θ - 4 (1 - sin^2 A) + 3 = 0

4 sin^2 A + 2 sin A - 1 = 0, which is a quadratic in sin A

- Therefore, sin θ = −2±−4(4)(−1)√2(4)

sin θ = −2±4+16√8

sin θ = −2±25√8

sin θ = −1±5√4

- Now sin 18° is positive, as 18° lies in first quadrant.

- Therefore, sin 18° = sin A = −1±5√4

(Good luck! I hope this helped. ^_^)