Find the value of
`(i) sin 18^(@) " "` (ii) `cos 18^(@) `
(iii) `cos 36^(@)" "` (iv) `sin36^(@)`
(v) `sin 72^(@)" " `(vi) `cos 72^(@) `
(vii) `sin54^(@)" "` (viii) `cos54^(@)`

Explanation

To find the values of the trigonometric functions for the angles given in the question, we will follow a systematic approach:

### Step 1: Find \( \sin 18^\circ \)

Let \( \theta = 18^\circ \). We know that \( 5\theta = 90^\circ \). We can express \( 5\theta \) as \( 2\theta + 3\theta \).

Using the sine addition formula:
\[
...