Question

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

Answer 1

[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.