Find the value of cos18°

FORMULA: - (i) in(90° – θ) = cosθ

(ii) sin2A = 2sinAcosA

(iii) cos3A = 4Cos³ A – 3 Cos A

(iv) sin2A + cos2A = 1

(v) for equation ax2 + bx + c

Let A = 18° then 5A = 90°

2A = 90° – 3A

Sin 2A = Sin (5A – 3A)

using formula (i)

sin2A = Sin (90° – 3A) = Cos 3A

using formula (ii) and (iii)

⇒ 2 Sin A Cos A = 4Cos³ A – 3 Cos A

⇒ 2 Sin A = 4 Cos² A – 3

⇒ 2sinA = 1 – 4 Sin² A

using formula (iv)

⇒ 4 Sin² A + 2 Sin A – 1 = 0

using formula (v)

using formula (iv)