Question

prove that: cosecA( secA-1)-cotA(1-cosA)=tanA-sinA

Answer 1

Here is your answer my friend
LHS=
cosecA(secA-1)-cotA(1-cosA)
1/sinA(1-cosA)/cosA - cosA/sinA(1-cosA)
take 1-cosA common
(1-cosA)(1/sinA•cosA-cosA/sinA)
(1-cosA)(sinA-sinA•cos^2A)/(sin^2A•cosA)
(1-cosA)(sin^2A)/(sin^2A•cosA)
(1-cosA)•tanA
tanA-sinA