SOLUTION: Verify the identity sin(x)/(1+cos(x))+(1+cos(x))/sin(x)=2csc(x)

Question 249656: Verify the identity
sin(x)/(1+cos(x))+(1+cos(x))/sin(x)=2csc(x)
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

Since the right side has 1 term and the left side has two terms, we will start by adding the terms on the left. Of course to add fractions we must have common denominators:

which simplifies:

Now we can add:

Since we get:

We now have a simplified, one-term expression on the left. Since the right side has a factor of 2, we'll factor out a 2 on the left:

As you can see, the (1 + cos(x))'s cancel leaving:

Since 1/sin(x) = csc(x) we have:

And we are finished.

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