1. Prove: cos x (csc x + tan x) = cot x + sin x.

2. Prove: sec B - cos B = tan B sin B.

3. Prove: sin = cos x.

4. Prove: .

5. Write cos 75° cos 15° + sin 75° sin 15° as a single trig function and then simplify.

6. Find the exact value of sin 15° using a sum or a difference formula.

7. Find the exact value of cos 105° using a sum or a difference formula.

8. If tan A = 3 with A in QI and tan B = -1/2 with B in QII, find
   tan (A + B).

    If cos A = -3/5 with A in QIII, find the value of:

9. .

10. sin 2A.

11. sec 2A.

12. 

13. Evaluate: cos (arctan 1/2 - arcsin 4/5)

14. Evaluate: cos (2 sin ^-1 x) and assume x is positive.

15. Rewrite cos 60° sin 30° as a sum or difference and then simplify if possible.