Southern New Hampshire University
MAT 140 Milestone Two: Second Practice Problem Walkthrough
[Steve D. Pettus
Southern New Hampshire University
Prove the identity:
cos(x-y =1+ tan x tan y cos x cos y
Going through the book that we have at SNHU to do our math problems, I think that it is in chapter number 5 of the text book we find some the problems that we need to solve what is called Trigonometric Identities that I'm going to use to show this equation like the sum and difference formulas for cosine which states cos(x-y)=cos x cos y + sin x sin y. Another way that sin x I going to try work out this problem is found in Quotient Identity which states tan = coS X and then we will be using some algebra to simplify the questions.
Now for this equation, I'm going to try and start off by saying that you choose one side of the problem to concentrate on. I'm going to start off with the left side of the problem and try to go through all of the necessary steps to make it alike or equal to the right side of the problem. I'm going to start by saying that you use the Sum and Difference Identity to rewrite the numerator like I put down in row number two on my table. The next thing that I will do to solve the equation will be to use algebra to cut the fraction in half as I have shown in row three of the table below. Looking at the left side of the fraction that is cut in half has the same numerator and denominator which I think is equal to the number one like shown in row number four of the table which is below. Now we began to split the rest of the fraction that is left like I put it down in sin x row number five. Now the big one Quotient Identity we are going to use it to replace CoS X with the tangent x. Then we turn right around and do the same thing for tangent y. This will bring us to the last row in the table below and it is going to be equivalent to the right side of the equation that was originally put down.
Southern New Hampshire University
Statement
Rule
cos(x-y) cos x cos y cos x cos y+sin x sin y cos x coS y
This will be on the left side of the equation
Sum and Difference
cos x cos y sin xsin y cos x cos y cos xcos y
Algebra (Cutting the Fraction in half)
sin x sin y 1+ cos x cos y
Algebra
Algebra
coS X 1+ cos y
1+tan x tan y
Quotient Identities
1 +tan x tan y
Equal to the right side of the equation
Gerken & Miller, 201