Given sin18° = (√5 − 1)/4 and cos36° = (√5 + 1)/4, the value of co$s^2$36° − si$n^2$18° is:

Use $a^2-b^2=(a+b)(a-b)$ with $a$ = (√5 + 1)/4 and $b$ = (√5 − 1)/4. Their sum is 2√5/4 = √5/2 and their difference is 2/4 = 1/2, so the product is √5/4 ≈ 0.559. Numerically 0.6545 − 0.0955 = 0.559. Stopping at the sum alone gives √5/2.