trignometry equations

[fiery123]

simplify
1/{1-[1/sin(90-x)]} - 1/{1+[1/sin(90-x)]}

sry if the brackets are confusing.

[Glaysher]

= 1/{1 - [1/cos x]} - 1/{1 + [1/cos x]}

= 1/[1 - sec x] - 1/[1 + sec x]

= [1 + sec x]/[(1 - sec x)(1 + sec x)] - [1 - sec x]/[(1 - sec x)(1 + sec x)]

= [1 + sec x - 1 + sec x]/[1 - sec² x]

= [2 sec x]/[1 - sec² x]

= [2 sec x]/[- tan² x]

= - (2/cos x) (cos² x/sin² x)

= - [2 cos x]/sin² x

= -2 cot x cosec x

[fiery123]

are you sure the answer says it is -2/(sinx tanx)? and of course i have no idea how to work it out. oh and what does sec stand for?

[da_silvy]

cot x = 1/tan x
cosec x = 1/sin x
sec x = 1/cos x

so his solution and your answer are exactly the same

[fiery123]

right thanks