(Cat A - cosec A +1) (1+sec A + tan A)
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(1+cot A-cosec A).(1+tanAtsecA)= 2
L.H.S.
=(1+cosA/sinA-1/sinA).(1+sinA/cosA+1/cosA)
=(sinA+COSA-1)×(cosA+sinA+1)/sinA.COSA
=[(sinA+cosA)^2-(1)^2]/sinA.cosA.
=(sin^2A+cos^2A+2.sinA.COSA-1)/sinA.COSA.
=( 1+2.sinA.COSA -1)/sinA.COSA.
= 2.sinA.cosA/sinA.cosA
= 2,
Hence proved.
Hope it helps you ❤
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