Rewrite the following using a single trigonometric function. You may wish to review your trigonometric identities in Chapter 1.

1. $10\operatorname{ sin}(3x)\operatorname{ cos}(3x)$

   Hint (a):

   Double Angle identity (factor first).

2. $\operatorname{sin }x\operatorname{ cos }3x −\operatorname{sin }3x\operatorname{ cos }x$

   Hint (b):

   Sum and Difference (Angle Sum) identity.

3. $\operatorname{cos}^4 x −\operatorname{ sin}^4 x$

   Hint (c):

   Factor first.

4. $\operatorname{tan }x +\operatorname{cot }x$

   Hint (d):

   Start by rewriting $\operatorname{tan}(x)$ and $\operatorname{cot }(x)$ as fractions.

   Hint 2(d):

   You will use more than one identity.

   Steps (d):

   $\frac{\text{sin}x}{\text{cos}x}+\frac{\text{cos}x}{\text{sin}x}=\frac{\text{sin}^{2}x+\text{cos}^{2}x}{(\text{cos}x)(\text{sin}x)}=$

   Answer (d):

   $\frac{1}{\frac{1}{2}\text{sin}(2x)}=2\text{csc}(2x)$