Please answer the following question?

(a)
LHS
= sin⁴θ + cos⁴θ
= sin⁴θ + 2sin²θcos²θ + cos⁴θ - 2sin²θcos²θ
= (sin²θ + cos²θ)² - (1/2) 2²sin²θcos²θ
= 1² - (1/2) (2sinθcosθ)²
= 1 - (1/2) sin²(2θ)
= RHS

(b)
sin⁴(π/16) + sin⁴(3π/16) + sin⁴(5π/16) + sin⁴(7π/16)
= sin⁴(π/16) + sin⁴(3π/16) + cos⁴(π/2 - 5π/16) + cos⁴(π/2 - 7π/16)
= sin⁴(π/16) + sin⁴(3π/16) + cos⁴(3π/16) + cos⁴(π/16)
= sin⁴(π/16) + cos⁴(π/16) + sin⁴(3π/16) + cos⁴(3π/16)
= [1 - (1/2) sin²(π/8)] + [1 - (1/2) sin²(3π/8)]    (by (a))
= [1 - (1/2) sin²(π/8)] + [1 - (1/2) cos²(π/2 - 3π/8)]
= [1 - (1/2) sin²(π/8)] + [1 - (1/2) cos²(π/8)]
= 1 + 1 - (1/2) [sin²(π/8) + cos²(π/8)]
= 2 - (1/2) (1)
= 2 - 1/2
= 3/2