(a + b)² = (2 + 3)² = 5² = 25.

a² + b² = 4² + 5² = 16 + 25 = 41.

Using the Pythagorean identity, sin B = √(1 - cos²B) = √(1 - 0.6²) = √(1 - 0.36) = √(0.64) = 0.8.

Cotangent is 1 when the angle A is 45°, as cot A = cos A/sin A = 1 when both are equal.

cot D = 3/4 implies tan D = 4/3. Therefore, sin D = 4/5 (using the identity sin²D + cos²D = 1).

tan A = sin A / cos A = (1/√2) / (1/√2) = 1.

Using the Pythagorean identity, cos C = √(1 - sin²C) = √(1 - 0.8²) = √(1 - 0.64) = √(0.36) = 0.6.

(a - b)(a + b) = a² - b², which is the difference of squares.

(x + y)(x - y) = x² - y², which is the difference of squares.

(2x + 3)² = 4x² + 12x + 9 by expanding the square of a binomial.

(a + b)² = a² + 2ab + b² by the expansion of the square of a binomial.

(x + 1)(x - 1) = x² - 1, which is the difference of squares.

According to the Pythagorean identity, sin² θ + cos² θ = 1 for any angle θ.

(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca.

(x - y)³ = x³ - 3x²y + 3xy² - y³ by the binomial theorem.

(x + y)³ = x³ + y³ + 3xy(x + y) by the binomial expansion.