Which expression is equivalent to sin(1.8x) sin(0.5x)? 0.5[sin(2.3x) + sin(1.3x)] 0.5[sin(2.3x) − sin(1.3x)] 0.5[cos(1.3x) − cos(2.3x)] 0.5[cos(2.3x) − cos(1.3x)]?

Hi, can anyone show me how to do this problem? 100 points for this. in advance

According to a study conducted in 2015, 18% of shoppers said that they prefer to buy generic instead of name-brand products. suppose that in a recent sample of 1500 shoppers, 315 stated that they prefer to buy generic instead of name-brand products. at a 5% significance level, can you conclude that the proportion of all shoppers who currently prefer to buy generic instead of name-brand products is higher than .18? use both the p-value and the critical-value approaches.

Consider the input and output values for f(x) = 2x - 3 and g(x) = 2x + 7. what is a reasonable explanation for different rules with different input values producing the same sequence?