hey!!
The given question should be as follows:-
(cosecA-sinA) (secA-cosA) = 1/(tanA+cotA).
L.H.S.
=(cosecA-sinA) (secA-cosA).
=(1/sinA-sinA)(1/cosA-cosA).
=(1-sin^2A) (1-cos^2A)/sinA.cosA.
=cos^2A.sin^2A/sinA.còsA.
=sinA.cosA/1.
=sinA.cosA/(sin^2A+cos^2A).
On dividing above and below by sinA.cosA.
=(sinA.cosA/sinA.cosA)/(sin^2A/sinA.cosA+cos^2A/sinA.cosA).
= 1/(tanA+cotA).
Hope it is clear and hope it would help you!