SOLUTION: please help prove the identity cos(u-v)/cos(u)sin(v)= tan(u)+cot(v) thank you!!!

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Question 240783: please help prove the identity
cos(u-v)/cos(u)sin(v)= tan(u)+cot(v)
thank you!!!

Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!

Since there is no (u-v) on the right side, we will use on the cos(u-v) giving us:

Since there are two terms on the right side, we will split the fraction on the left into two terms. (Think of it as "unadding".):

As you can see, we can do some canceling in each fraction:

leaving:

Since cos(v)/sin(v) = cot(v) and sin(u)/cos(u) = tan(u) we can substitute and get:

And, using the Commutative Property of Addition, we can change the order on the left to:

And we are done.

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