三角證明題

RHS=secx-tanx/cosecx-cotx
=1/cosx-sin²x/cosx-cosx/sinx
=(sinx-sin³x-cos²x)/sinxcosx
=(cosecx-sinx-cot²x)/cotx (Divide sin²x on both denominator and nominator)
=cosecx+cos²x/sinx+tanx
=cosecx+cotx/secx+tanx
=LHS

考慮
(csc x + cot x/sec x + tan x) - (sec x- tan x/csc x - cot x)
=1/sin x + (cos x/sin x)(1/cos x) + sin x/cos x - 1/cos x + (sin x/cos x)(1/sin x) + cos x/sin x
=1/sin x + 1/sin x + sin x/cos x - 1/cos x + 1/cos x + cos x/sin x
=2/sin x + sin x/cos x + cos x/sin x
=2/sin x + 1/(sin x)(cos x)

不等於0