Question

Prove that
Cos 36 - sin 18° = 1/2​

Answer 1

Step-by-step explanation:

Cos 36 = Sin 54

Cos 36 - Sin 18 = Sin 54 - Sin 18

Sin A - Sin B = 2 sin ½ (A − B) cos ½ (A + B)

= 2 sin ½ (54 − 18) cos ½ (54 + 18)

= 2 sin ½ (36) cos ½ (72)

= 2* Sin 18 * Cos 36 ------(1)

Sin 2A = 2 Sin A Cos A

let's take A is 18

Sin 36 = 2* Sin 18 * Cos 18

sin(18)=sin(36)/(2∗cos(18))

Sub in (1)

=> cos(36)∗sin(36)/cos(18)

Cos 18 = Sin 72

and cos(36)∗sin(36) = 0.5* Sin 72

=> 0.5* Sin 72/ Sin 72

= 1/2

Hence proved.

Hope you are satisfied with the solution.