Verify the Identity:

Question

sin(x+π)/cos(x+3π/2) =tan^2x-sec^2x

I've done:
sinxcosπ+cosxsinπ
/
cosxcos(3π/2) - sinxsin(3π/2)

sinx(-1) + cosx(0)
/
cosx(0)- sinx(-1)

-sinx/sinx

What do I do from here? Or what did I do wrong?

Answer 1

first, note that since sec^2 = 1+tan^2, the right side is just -1

On the left, you have arrived at sinx/sinx = -1

Done

Answer 2

thank you!