Question

How do you simplify the expression `costhetasectheta-costheta/sectheta`?

Answer 1

Apply the identity `secbeta = 1/cosbeta`.

`=costheta xx 1/costheta - costheta/(1/costheta)`

`=cancel(costheta) xx 1/cancel(costheta) - costheta xx costheta`

`= 1 - cos^2theta`

Apply the identity `sin^2theta + cos^2theta = 1`:

`=sin^2theta`