Prove that 1/(tanx) + tanx = 1/sinxcosx

The key here is to realise that tanx = sinx/cosx. If we write out the left hand side of the equation in terms of sine and cosine we get: cosx/sinx + sinx/cosx These two fractions can be put over a common denominator of sinxcosx to give: (cos²x + sin²x)/sinxcosx If we then use the well-known identity cos²x + sin²x = 1, we see that the above expression is equivalent to 1/sinxcosx, which is the expression we were required to find.