Sin 45° + sin 60° sin 45° - sin 60° sin 45° : sin 60° sin 45° × sin 60° √2 × sin 45° √3 × sin 60° (sin 60°)⁴ (sin 45°) sin 45° : sin 30°

Sin 45° + sin 60° = √2/2 + √3/2 = (√2+√3)/2
sin 45° - sin 60° = √2/2 - √3/2 = (√2-√3)/2
sin 45° ÷ sin 60° = √2/2 ÷ √3/2 = √2/2 × 2/√3 = √(2/3)
sin 45° × sin 60° = √2/2 × √3/2 = √6/4
√2 × sin 45° = √2 × √2/2 = 2/2 = 1
√3 × sin 60° = √3 × √3/2 = 3/2 = 1.5
(sin 60°)⁴ = (√3/2)⁴ = 9/16
(sin 45°) = √2/2
sin 45° ÷ sin 30° = √2/2 ÷ 1/2 = √2/2 × 2 = √2