Set P = {2, 4, 6, 8} and set Q = {2, 3, 5, 7}. The union is {2, 3, 4, 5, 6, 7, 8}.

The symmetric difference of sets R and S includes elements that are in either set but not in both. Thus, it is {1, 2, 3, 6, 7}.

The difference R - S includes elements in R that are not in S, which is {1, 2}.

The difference T - U includes elements that are in set T but not in set U, which is {1}.

The symmetric difference of sets T and U is {1, 4}, which includes elements that are in either set but not in both.

The hybrid set formed by combining sets X and Y includes all unique elements from both sets, resulting in {1, 2, 3, 4, 5}.

The union of sets X and Y includes all unique elements from both sets. Thus, the union is {a, b, c, d}.

The hybrid set formed by the union of set X and set Y includes all unique elements from both sets, which are {1, 2, 3, 4, 5}.

The union of set X and set Y includes all unique elements from both sets, resulting in {1, 2, 3, 4, 5}.

The intersection of set X and set Y is {3}, as it is the only element common to both sets.

The double angle formula for cosine is cos 2A = cos²A - sin²A.

Using the double angle formula, sin 2A = 2(1/2)(√(1 - (1/2)²)) = 2(1/2)(√(3/4)) = 1.

Sin A = 0 at A = 0°, 180°, and 360°. The principal value is 0°.

Using the identity sin^2 A + cos^2 A = 1, we have cos A = sqrt(1 - (0.6)^2) = sqrt(1 - 0.36) = sqrt(0.64) = 0.8.

Using the Pythagorean identity, cos A = √(1 - sin²A) = √(1 - 0.36) = √(0.64) = 0.8.

Using the identity sin^2 A + cos^2 A = 1, we have cos A = sqrt(1 - (0.6)^2) = sqrt(1 - 0.36) = sqrt(0.64) = 0.8.

Using the identity tan A = sin A / cos A, we find cos A = sqrt(1 - (0.6)^2) = 0.8, thus tan A = 0.6 / 0.8 = 0.75.

sin A = 1/2 at A = 30° and A = 150°.

sin A = 1/2 corresponds to A = 30°.

The angle A for which sin A = 1/2 is π/6 radians.

In the first quadrant, sin A = 1/2 corresponds to A = 30°.

The angle A for which sin A = 1/√2 is A = 45°.

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

Using the identity sin^2 A + cos^2 A = 1, we have cos A = sqrt(1 - (3/5)^2) = sqrt(1 - 9/25) = sqrt(16/25) = 4/5.

Using the identity tan A = sin A / cos A, we find cos A = 3/5, thus tan A = (4/5) / (3/5) = 4/3.

Using the Pythagorean identity, cos A = √(1 - sin²A) = √(1 - (5/13)²) = √(1 - 25/169) = √(144/169) = 12/13.

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

Using the Pythagorean identity, cos θ = √(1 - sin²θ) = √(1 - 0.8²) = √(1 - 0.64) = √(0.36) = 0.6.

The double angle formula for sine is sin(2x) = 2sin(x)cos(x).

This is known as the Double Angle Identity for sine.