1. ## Quick Question Help

I am doing a non-credit assignment and would like to check my answers to see if I have done them correctly, If you can provide help, show steps and/or show me final answer to the following questions it would greatly assist me to see if I am doing these correctly, Thank you!
Question 1:
The exact value of cos(105) can be determined using the sum and difference identities. Determine the exact value of cos(105) and express the answer in the form
$\frac{\sqrt{\alpha }-\sqrt{\beta }}{\zeta }$

Question 2:
Prove the Following algebraically;

$\frac {tanx}{cscx-cotx}=secx+1$

Question 3:
Solve the following equation $Sin(3x)=\frac {1}{2}-$ for x, where $0\leq X\leq 360$

2. ## Re: Quick Question Help

For the first one.

$\cos 105 = \cos (60+45)$

Now apply the identity $\cos (A+B) = \cos A \cos B - \sin A \sin B$

3. ## Re: Quick Question Help

Originally Posted by Prentz
I would like to check my answers to see if I have done them correctly.

4. ## Re: Quick Question Help

Question 3 To get values of x in range 0-360 you need to consider 3x in range 0-1080
Hence 3x=30,150,390,510,750,870

5. ## Re: Quick Question Help

Write tanx as sinx/cosx, cscx as 1/sinx and cotx as cosx/sinx. Then multiply top and bottom by sinxcosx.
Should then get sin^2x/cox-cos^2x. Now write sin^2x as 1-cos^2x which factorises to (1-cosx)(1+cosx). Also factorise cosx-cos^2x into cosx(1-cosx). You should see that (1-cosx) cancels out and get the result.