Question

Find the values of sin 18and cos 18.

Answer 1

Answer:

Answer is given in the above attachment.

Answer 2

Answer:

1.

Let θ = 18°. Then

5θ = 90°

∴ 2θ + 3θ = 90°

⇒ 2θ = 90° – 30°

⇒ sin 2θ = sin (90° – 3θ) = cos 3θ

⇒ 2 sin θ cos θ = 4 cos3θ – 3 cos θ

⇒ 2 sin θ cos θ – 4 cos3θ + 3 cos θ = 0

⇒ cos θ (2 sin θ – 4 cos2 θ + 3) = 0

⇒ 2 sin θ – 4 (1 – sin2θ) + 3 = 0 (cos θ = cos 18° ≠ 0)

⇒ 4sin2 θ + 2 sin θ – 1 = 0

2.

We know that,

sin2 18° + cos2 18° = 1

∴ cos2 18° = 1 – sin2 18°