When verifying trigonometric identities, it's best to convert everything to sine and cosine if at all possible.

Here's some basic identities

sin^2(x) + cos^2(x) = 1
1 + tan^2(x) = sec^2(x)
1 + cot^2(x) = csc^2(x)

You can use properties of equality on the identities as follows:

1 - cos^2(x) = sin^2(x)
1 - sin^2(x) = cos^2(x)

tan^2(x) = sec^2(x) -1
cot^2(x) = csc^2(x) - 1


Remember that tanx = sinx/cosx

cotx = cosx/sinx/ 

         = 1/tanx

cscx = 1/sinx

secx = 1/cosx


sin(x + y) = sinxsiny + cosxcosy