Trig proofs
how do you solve:

tanx + cotx = secxcscx

Useful identities (memorize them)

tan(x) = \frac {sin(x)}{cos(x)} (1)

cot(x) = \frac {1}{tan(x)} = \frac {cos(x)}{sin(x)} (2)

sec(x) = \frac {1}{cos(x)} (3)

csc(x) = \frac {1}{sin(x)} (4)

cos^2(x) + sin^2(x) = 1 (5)

So, your problem is:

tan(x) + cot(x) = sec(x)csc(x)

\frac {sin(x)}{cos(x)} + \frac {cos(x)}{sin(x)} = \frac {1}{cos(x)} \times \frac {1}{sin(x)}

Take the left hand side and find the common denominator. Use identity #5, above, and you'll find that the two sides are equal, which is what you want to prove.