Answer:
see explanation
Explanation:
using the identity
sin²t + cos²t = 1
consider the left side
(cost - 2sint)² + (2cost + sint)² ← expand factors using FOIL
= cos²t - 4sintcost + 4sin²t + 4cos²t + 4sintcost + sin²t ← collect like terms
= 5sin²t + 5cos²t ← factor out 5 from each term
= 5(sin²t + cos²t)
= 5 × 1
= 5
= right side , thus verified