Since some birds can fly and sparrows are included in the category of birds, it is true that some sparrows can fly.

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

'Barking up the wrong tree' means to pursue a mistaken or misguided course of action.

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

'Under the weather' is an idiom that means someone is feeling ill or unwell.

'Under the weather' means feeling ill or unwell.

'Meticulous' means showing great attention to detail.

'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.

'Spill the beans' means to reveal confidential information or secrets.

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

'On cloud nine' is an idiom that signifies being in a state of extreme happiness.

The idiom 'under the weather' means feeling ill or unwell.

'Arduous' means involving or requiring strenuous effort; difficult and tiring.

Since T is between U and V, U is next to V. W being opposite T does not change this adjacency.

Since T is between U and V, the person sitting next to U must be V.

There is no information provided about who is next to V.

The arrangement U T W V is valid as T is next to U and V is next to W.

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

If T is the father of U and U is the son of V, then V is T's wife.

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.

Since tan θ = sin θ / cos θ, and tan θ = 1/√3, we can use the 30-60-90 triangle where 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°.