math help PLEASE!!?

Question

1) find the angle between the lines y=2x+1 and y= -3-5
what are the steps to find the answer?

2) simplify: (1-cos^2x)(1-cot^2x)
??? please help me!!

Answer 1

1) I assume the second line is actually y = -3x - 5. The first line has slope 2 and the second line has slope 3. A line's slope is equal to the angle the line makes with the positive x-axis. From the horizontal, the first line has an angle of arctan(2) and the second has an angle of arctan(-3). The first line should have a positive angle less than 90 degrees, and the second line should have a negative angle greater than -90 degrees. The angle between the lines is arctan(2) - arctan(-3).

2) (1 - cos^2(x))(1 - cot^2(x)) = (sin^2(x))(1 - (cos^2(x))/(sin^2(x))) = sin^2(x) - cos^2(x) = -cos(2x)

Answer 2

go to your library and find a trigonometry book... you can find an answer there...