Ask Me Help Desk - Trig proofs

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.