Question

how to find the value of cos36?

Answer 1

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 cos33 A - 3 cos A

⇒ 2 sin A cos A - 4 cos33 A + 3 cos A = 0

⇒ cos A (2 sin A - 4 cos22 A + 3) = 0

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

⇒ 2 sin θ - 4 (1 - sin22 A) + 3 = 0

⇒ 4 sin22 A + 2 sin A - 1 = 0, which is a quadratic in sin A

Therefore, sin θ = −2±−4(4)(−1)√2(4)244124
⇒ sin θ = −2±4+16√824168
⇒ sin θ = −2±25√82258
⇒ sin θ = −1±5√4154
Now sin 18° is positive, as 18° lies in first quadrant.

Therefore, sin 18° = sin A = −1±5√4154
Now, cos 36° = cos 2 ∙ 18°

⇒ cos 36° = 1 - 2 sin22 18°

⇒ cos 36° = 1 - 2(5√−14)25142
⇒ cos 36° = 16−2(5+1−25√)16162512516
⇒ cos 36° = 1+45√1614516
⇒ cos 36° = 5√+14514
Therefore, cos 36° = 5√+14514

Answer 2

i think you have to learn the value of cos18 cos36 sin18 sin36.....the value of cos 36 is underroot 5+1/4