Prove the following identity:
tan(theta) sin(theta) + cos(theta) = sec(theta) for real numbers theta, where theta ≠ / 2 + , for all integers k.

Astudent draws two parabolas on graph paper. both parabolas cross the x-axis at (–4, 0) and (6, 0). the y-intercept of the first parabola is (0, –12). the y-intercept of the second parabola is (0, –24). what is the positive difference between the a values for the two functions that describe the parabolas? write your answer as a decimal rounded to the nearest tenth