Simplify

sin (180-theater). cos (90°-theater) - 1/cos (-theater)

[sin (180-a) x cos (90-a) - 1]/cos (-a)

= [sin (a) x sin (a) - 1] / (-cos (a))

= [sin^2 (a) - 1] / (-cos (a))

= [-cos^2 (a) ] / (-cos (a))

= cos (a)

formula used

sin (180-a) = sin (a)

cos (90-a) = sin (a)

cos (-a) = - cos (a)

sin^2 (a) + cos^2 (a) = 1

all of these are easily proved by the unit circle. you might find someone to explain this. it will be very handy.