sin(θ) = 1/√2 at θ = 45° and θ = 225°.

sin(θ) = 1/√2 at θ = 45°.

sin(45°) = 1/√2, so θ = 45°

Using the Pythagorean identity, cos(θ) = √(1 - sin²(θ)) = √(1 - (3/5)²) = 4/5.

Using the identity tan(θ) = sin(θ)/cos(θ) and cos(θ) = √(1 - sin^2(θ)), we find cos(θ) = 3/5. Thus, tan(θ) = (4/5)/(3/5) = 4/3.

The equation sin^(-1)(x) + cos^(-1)(x) = π/2 holds for all x in the domain of the functions, which is [-1, 1]. Therefore, x can be any value in this range.

Using the identity sin^(-1)(x) + cos^(-1)(x) = π/2, we can conclude that x can take any value in the range [-1, 1].

If sin^(-1)(x) = π/4, then x = sin(π/4) = √2/2.

If cos A = 0, then sin²A = 1 - cos²A = 1 - 0 = 1.

Since some fruits are apples and all apples are sweet, it follows that some fruits are sweet.

'On cloud nine' means to be in a state of blissful happiness.

'Under the weather' means feeling ill or unwell.

'Burn the midnight oil' means to stay up late working or studying.

'Hit the nail on the head' means to describe exactly what is causing a situation or to be very accurate in one's assessment.

'Let the cat out of the bag' means to accidentally reveal a secret.

'A chip on their shoulder' means to have a grudge or to be angry about something.

V is the brother of T as both are children of U.

S is to the left of T.

Using the identity tan A = sin A / cos A, we can find sin A = tan A * cos A. Using the Pythagorean identity, we find sin A = 3/5.

Since tan θ = sin θ / cos θ and tan θ = 1, we have sin θ = cos θ. For θ = 45°, sin θ = 1/√2.

If tan(x) = 1, then sin(x) = cos(x). Therefore, sin(x) + cos(x) = 2sin(x) = 2(1/√2) = √2.

tan(45°) = 1, hence x = 45°.

Using the identity tan(x) = sin(x)/cos(x), we can find sin(x) = 3/5 after applying the Pythagorean theorem.

Using the identity tan(x) = sin(x)/cos(x), we can find sin(x) = 3/5 after calculating the hypotenuse using the Pythagorean theorem.

tan(θ) = 1 at θ = 45°.

tan(45°) = 1, so θ = 45°.

Using the identity sin²(θ) + cos²(θ) = 1, we find sin(θ) = 3/5.

tan^(-1)(x) = π/4 implies that x = tan(π/4) = 1.

A, B, C is the correct sequence as it respects the order of dependencies.

The condition states that B cannot start until A is completed, making this the only valid conclusion.