Sin18°=?

1.	Sin18°=?
Answer» Let A = 18° Therefore, 5A = 90° ⇒ 2A + 3A = 90˚⇒ 2θ = 90˚ - 3ATaking 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 ATherefore, sin θ = −2±−4(4)(−1)√2(4)⇒ sin θ = −2±4+16√8⇒ sin θ = −2±25√8⇒ sin θ = −1±√5/4Now sin 18° is positive, as 18° lies in first quadrant.Therefore, sin 18° = sin A = −1±√5/4

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