General Knowledge: Sports, Literature & Math

Surrey County Cricket Club uses 'Brown Caps' as one of their traditional nicknames, referring to their brown caps worn in the past. The other options are nicknames of other counties: Bears (Warwickshire), Foxes (Leicestershire), Outlaws (Nottinghamshire).

The tangent function is defined as tan x = sin x / cos x, which is the ratio of sine to cosine for the same angle. Options A and B are incorrect reciprocals, while D would be cotangent (cot x = cos x / sin x).

The Pythagorean identity states that sin²x + cos²x = 1 for any angle x. This is one of the fundamental identities in trigonometry derived from the unit circle definition. Options 0, 90, and -1 are incorrect values for this expression.

Cosine is an even function, meaning cos(-x) = cos x for all x. This symmetry property holds because cosine is based on the x-coordinate on the unit circle, which is unchanged by reflecting across the x-axis. Sine is odd (sin(-x) = -sin x).

The cosine addition formula is cos(x+y) = cos x cos y - sin x sin y. This is a fundamental trigonometric identity for expanding cosine of a sum. Option A has the wrong sign, B mixes sine and cosine incorrectly, and D just reorders the terms but still has the wrong sign.

cos 0° = 1 because at angle 0 on the unit circle, the point is (1, 0), and cosine represents the x-coordinate. This is a fundamental value in trigonometry. Options 0, -1, and -1/2 are incorrect.

The double-angle formula for sine is sin 2x = 2 sin x cos x. This identity can be derived from the sine addition formula sin(x+x) = sin x cos x + cos x sin x. Option B is missing the factor of 2, and the other options are incorrect.

sin(180° - x) = sin x due to the supplementary angle identity. In the second quadrant (angles 90° to 180°), sine is positive and has the same value as its supplement. This is related to the symmetry of the sine function.

The secant function is defined as sec x = 1/cos x, the reciprocal of cosine. Option D (1/sin x) would be cosecant (csc x), and options A and B are incorrect expressions. This is a fundamental reciprocal identity in trigonometry.

tan(45°) = sin(45°)/cos(45°) = (√2/2)/(√2/2) = 1. At 45 degrees, sine and cosine have equal values, so their ratio is 1. Infinity would mean cos(45°) = 0, which is false.

cos(60°) = 1/2. In the special 30-60-90 right triangle, the side adjacent to the 60° angle is half the hypotenuse. cos(0°) = 1 and cos(90°) = 0, so 1/2 is the correct intermediate value.

Sine is an odd function, meaning sin(-x) = -sin(x). The graph of sine is symmetric about the origin, so the negative angle produces the negative of the original value. This is a fundamental trigonometric identity.

Edmond Dantès is the protagonist of Alexandre Dumas' 'The Count of Monte Cristo'. He is wrongfully imprisoned on his betrothal day, escapes after 14 years, and seeks revenge against those who framed him, including his friend Pharon who turned against him.

Mr. Fitzwilliam Darcy is the male protagonist of Jane Austen's 'Pride and Prejudice'. He initially refuses to dance with Elizabeth Bennet, appearing proud, but later falls in love with her and helps resolve the crisis when Lydia elopes with Wickham.

David Copperfield is the autobiographical protagonist of Charles Dickens' novel. His mother dies, he marries the childish Dora who dies within a year, and he eventually marries Agnes whom he had loved like a sister while thwarting the villainous Uriah Heep.

This poem appears in Robert Louis Stevenson's 'Treasure Island', sung by the pirates. The 'Dead Man's Chest' is a location in the story, and the song captures the lawless, dangerous life of pirates. The novel features Long John Silver and Jim Hawkins.

The Tasmanian Tigers represent the state of Tasmania in Australian domestic cricket. The 'Tigers' nickname has been used historically by Tasmania's cricket team. The other options are team names from different states - Bulls (Queensland), Redbacks (Southern Australia), and Warriors (Western Australia).

Western Australia's cricket team is called the Western Warriors. The Warriors represent Western Australia in domestic cricket competitions. The Blues are from NSW, Hawks are from Tasmania (historically), and Redbacks are from Southern Australia.

Queensland's cricket team is known as the Queensland Bulls. The Bulls represent Queensland in Sheffield Shield and other domestic competitions. The Blues are from NSW, while Foxes and Steelbacks are not Australian state teams.