Thread: Proving Identities

I am having problems with proving identities. Could someone please help me?

1. tanx + cot x = secxcscx

2. sec^2x = ___cscx____
cscx - sinx

3. _tan^2t__ = sect - cost
sect

We first need to know these three facts,

tan x = sin x / cos x
cotan x = cos x / sin x
(sin x)^2 + (cos x)^2 = 1
Then,
tan x + cotan x = (sin x / cos x) + (cos x / sin x)
= ((sin x)^2 + (cos x)^2)/(sin x * cos x)
= 1 / (sin x * cos x)
= (1/sin x)*(1/cos x)
= csc x sec x = sec x csc x

Get the idea now? When dealing with sec x and csc x it is usually easier to put them in terms of sine and cosine and just grind through the algebra.