Rita is proving that the following trigonometric identity is true: cos(−θ)sin(−θ)=−1tanθ Which step would be the first line of her proof? cosθsinθ=−1tanθ cosθ−sinθ=−1tanθ cos(−θ)sinθ=−1tanθ cos(−θ)⋅tanθ=sin(−θ) please answer I have no idea how to do this WILL MARK BRAINLIEST

Two line segments are shown in the figure below. suppose that the length of the line along the x-axis is 6, and the length of the hypotenuse of the triangle is 10. what is the equation of the hypotenuse line (shown in red, below)?

Yahir designs bracelets. he uses between 9 and 15 red and yellow beads in the ratio of 2 red bead to 5 yellow beads. drag the beads into the container to meet these requirements

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.