Write each expression in terms of sine and cosine. and then simplify so that no quotients appear in the final expression and all functions are of theta only. csc^2 theta - 1/1 + cot^2 theta csc^2 theta - 1/1 + cot^2 theta =

12x + 1 = 25 solve the following equation. then place the correct number in the box provided.

Asays "we are both knaves" and b says nothing. exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by smullyan [sm78]) who can either lie or tell the truth. you encounter three people, a, b, and c. you know one of these people is a knight, one is a knave, and one is a spy. each of the three people knows the type of person each of other two is. for each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. when there is no unique solution, list all possible solutions or state that there are no solutions. 24. a says "c is the knave," b says, "a is the knight," and c says "i am the spy."

Which number line represents the solution set for the inequality -1/2x> 24?