please use matlab and show the code and output

Exercise M5 Consider the following function ().where time t is measured in seconds: f(0) = 15.cos(80t + 1.2) cos(120t - 1.8) Look up the formula for turning the product of two sinusoids into the sum of two sinusoids. Include an appropriate citation near the beginning of your script. Write the identity in a comment near the beginning of your script, using the same symbols used in your citation. (You can change aand pto a and bor A and B.) Write a MATLAB script that will demonstrate that a product of two sinusoids can be written as the sum of two sinusoids. Do this by graphing all three functions on one figure, i.e. ) and the two sinusoids whose sum should be equal to C), from t= -100ms tot = 100ms, then by graphing a "checking" function that should be an array of zeros if the identity is correct. Think about how you can compute the three functions efficiently. (HINT: Look at the identity you are using, and define two simple functions that you can use to define all three functions to plot.) There will also be an overall factor that you can define then use three times. There are actually two checks: (1) Construct a "checking" function that should be an array of zeros if the identity is correct. Plot this function on the same figure as the other three functions. (2) Use the ABS (absolute value) and SUM functions to design a check that is a single number that should be close to zero ONLY (and I mean only) if every single one of the elements of the "checking" function array is close to zero. Comment in your script why you think you are using the ABS function to accomplish this design criterion, rather than using only the SUM function, and output this value to the Command Window. (Think about what can go wrong when using only the SUM function.) Make sure there is a proper legend, a meaningful title, and appropriate axis labels on your figure. The legend text should be in the form, "I = (something)","11 = [first part of something else)"...."check= [your expression), should be 0". Use the YLIM command to make room for the legend, so that it does not cover up any of your graphs. Make sure the line widths and font sizes are appropriate to the size of the figure. The title should be in the form "Showing that (something) can be written as something else)". Use a multiline title, e.g, the context on one line and the description on the next one or two lines