I have a couple questions that I need a little direction on.

1:

Prove that

Method:

I figured out that I should convert to . But beyond that, I'm a little lost....I know there is more to be done though. I just don't quite understand how reciprocal and Pythagorean identities are related, I know that but I'm not sure if the same holds true for their Pythagorean counterparts or if that would be a valid proof.

2:

Prove that .

Method:

I made the equation into .

Does the equation become , or am I missing something?

I think I have the right answer, as I see that the Pythagorean identity for coinsides with my converted equation.

3:

Find the exact value of with out using tables or a calculator.

Be sure to show your work.

Method:

Since the question asks for the value of a unusual degree measure I have to use an addition formula, namely: .

For \alpha I used value 135 and for \beta I used 30 so , therefore the whole formula changes to become: .

So, , have I gotten the right answer?

4:

Find the direct value of without using tables or a calculator.

Be sure to to show your work.

Method:

The book said nothing about the addition formula for so I searched the internet and found this:

I decided to use this formula since I could figure out no other to use, I entered for and for , but I dont know where to go from here....

Thanks.