Verify the trigonometric identities 1) (sin x + cos x)^2 + (sin x - cos x)^2=2 2) (2 - cos^2 x) / (sin x) = csc x + sin x 3) (cos x-sin^2 x) / (sin x + cos^2 x) = (csc x - tan x) / (sec x + cot x) these are the rest of the instructions: for each of the following problems, verify that the left-hand side of the equation is equal to the right-hand side of the equation. try to simplify the side that is most complex and get it to equal the other side. if you come to a point where you are unable to continue, you may have to start over and simplify the other side instead. show work so i can figure out how to do this problem in the future!

The weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. use this distribution as a model for time (in hours) to failure of solid insulating specimens subjected to ac voltage. the values of the parameters depend on the voltage and temperature; suppose α = 2.5 and β = 190. (a) what is the probability that a specimen's lifetime is at most 250? less than 250? more than 300? (round your answers to four decimal places.) at most 250 less than 250 more than 300 (b) what is the probability that a specimen's lifetime is between 100 and 250? (round your answer to four decimal places.) (c) what value is such that exactly 50% of all specimens have lifetimes exceeding that value? (round your answer to three decimal places.) hr