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

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

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

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}.

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 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 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 C = √(1 - sin²C) = √(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.

sin(x) = 0 at x = nπ, where n is any integer.

If sin(x) = 0, then cos(x) can be either 1 or -1 depending on the angle x.

tan(x) = sin(x)/cos(x). If sin(x) = 0, then tan(x) is undefined when cos(x) = 0.

sin(x) = 0 at x = nπ, where n is any integer, hence all of the above.

The angles where sin(x) = 1/2 are x = π/6 and x = 5π/6.

sin(x) = 1/2 at x = π/6 and x = 5π/6 in the interval [0, 2π].

sin(30°) = 1/2, so x = 30°.

The angles where sin(x) = 1/2 in the interval [0, 2π] are x = π/6 and x = 5π/6.

x = π/6 and 5π/6.

Using the identity sin^2(x) + cos^2(x) = 1, we have cos^2(x) = 1 - (1/√2)^2 = 1 - 1/2 = 1/2. Thus, cos(x) = ±1/√2.

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

Using the identity sin^2(x) + cos^2(x) = 1, we have cos^2(x) = 1 - (1/√2)^2 = 1 - 1/2 = 1/2. Therefore, cos(x) = 1/√2.

Using the identity sin^2(x) + cos^2(x) = 1, we have cos^2(x) = 1 - (3/5)^2 = 1 - 9/25 = 16/25. Therefore, cos(x) = ±4/5. The positive value is taken as x is in the first quadrant.