Let S be the set of all real values of x with 0 < x < pi/2 such that sin x, cos x, and tan x form the side lengths (in some order) of a right triangle. Compute the sum of tan^2 x over all x in S.

Solve the problem by using a venn diagram a group of students were surveyed about their taste in music.they were asked how they like three types of music: rock, country western and jazz.the results are summarized below: no one dislikes all three types of music.six like all three types of music.eleven don’t like country western.sixteen like jazz.three like country western and jazz, but not rock.six don’t like rock.eight like rock and country western.seven don’t like jazz.how many students were surveyed?