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!

1) you deposit $2,500 in an account that earns 4% simple interest. how much do you earn in eight years?

Need this at the city museum, child admission is 6 and adult admission is 9.20. on tuesday, 132 tickets were sold for a total sales of 961.60. how many adult tickets were sold that day?

Evaluate 8x2 + 9x − 1 2x3 + 3x2 − 2x dx. solution since the degree of the numerator is less than the degree of the denominator, we don't need to divide. we factor the denominator as 2x3 + 3x2 − 2x = x(2x2 + 3x − 2) = x(2x − 1)(x + 2). since the denominator has three distinct linear factors, the partial fraction decomposition of the integrand has the form† 8x2 + 9x − 1 x(2x − 1)(x + 2) = correct: your answer is correct. to determine the values of a, b, and c, we multiply both sides of this equation by the product of the denominators, x(2x − 1)(x + 2), obtaining 8x2 + 9x − 1 = a correct: your answer is correct. (x + 2) + bx(x + 2) + cx(2x − 1).