Evaluate: (i) sin²63° + sin²27°cos²17° + cos²73° (ii) sin25°cos65° + cos25°sin65°

(i)We know that cos(90° - θ) = sinθ, sin(90° - θ) = cosθ
sin63° = sin(90° - 27°) = cos27°
And, cos17° = cos(90° - 73°) = sin73°
∴sin²63° + sin²27°cos²17° + cos²73° = cos²27° + sin²27°cos²73° + cos²73°
= cos²27° + sin²27° + cos²73°
= 1 + cos²73°
This is incorrect. The correct approach is:
sin²63° + sin²27° + cos²73° = sin²63° + cos²63° + cos²73° = 1 + cos²73° This is still not simplified completely.
Let's re-examine the problem. It seems there's a misinterpretation. The problem likely intends for the expression to simplify to 1.
Let's assume the question is: sin²63° + sin²27°cos²17° + cos²73°
Using trigonometric identities: sin²θ + cos²θ = 1
Then sin²27° + cos²27° = 1 and sin²63° + cos²63° = 1
However, this doesn't directly simplify the given expression to 1.

(ii)We know that cos(90° - θ) = sinθ, sin(90° - θ) = cosθ
sin25° = sin(90° - 65°) = cos65°
cos25° = cos(90° - 65°) = sin65°
∴sin25°cos65° + cos25°sin65° = cos65°cos65° + sin65°sin65° = cos²65° + sin²65° = 1