How do you find the value of #tan(csc^-1(2))#?
First you need to find the angle that corresponds to a csc value of 2, which is what inverse csc is doing.
So find when cos is 1/2, which is at
Then plug in
Use the identity:
Please see this reference section Relationships between trigonometric functions and inverse trigonometric functions. I am referring you to this section because it contains a table that will help you if your current studies require you to do many problems of this type.
The table gives the following identity:
Please notice that there is a nice triangle drawing to the right within the table:
Rationalize the denominator: