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a.
(sin ∝ - cos ∝)^2 + (2sin ∝ + cos ∝)^2
= sin^2 ∝ + cos^2 ∝ - 2.sin ∝.cos ∝ + 4sin^2 ∝ + cos^2 ∝ + 4.sin ∝.cos ∝
= 1 + 2.sin ∝.cos ∝ + 1 + 3. sin^2 ∝
= 2 + 2.sin ∝.cos ∝ + 3.sin^2 ∝
b.
cot 44° . cot 45° . cot 46°
= (tan 46° . cot 46°) . cot 45°
= 1 . cot 45°
= 1 . 1
= 1