For this question you need to be aware of some of the trigonometric identities, which include the pythagorean identities and the double angle identities.

Since we are aware that sin2x=2sinxcosx and 1 + tan²x= sec²x, we will begin with using these to simplify our fraction.

= 2sinxcosx/(1 + tan²x)

**Step 2: Replace (1 + tan²x) with sec²x**

= 2sinxcosx/sec²x

**Step 3: Since secx=1/cosx, so sec²x= 1/ cos²x. Hence you replace sec²x in the equation now**

= 2sinxcosx/(1/cos²x)

**Step 4: Take the reciprocal of 1/cos²x, which basically involved switching the numerator with the denominator and vice versa**

= 2sinxcosx(cos²x)

= 2sinxcos³x