(cosecA-sinA)(secA-cosA)=1\cotA+tanA
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Step-by-step explanation:
(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).
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