You first three methods are correct.
Last one,
tan15 = (tan45 - tan30)/(1-tan45*tan30)
Substitute the values to get tan 15.
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.
Ok! Thank you!
Just curious, but is there a simpler way to do this question?
I know I can and will do it this way--don't get me wrong, but my text book said nothing about this way of solving the question, so I think that they may want a different method to be used. Like I said, they did not give one though...