Question

please prove this
20. Prove that: (a) (cos ecA - sin A)(sec A-COS A)(tan A + COS A)=1
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Answer 1

LHS

=(tanA+cotA).(cosecA-sinA).(secA-cosA)

=(sinA/cosA+cosA/sinA).(1/sinA-sinA).(1/cosA-cosA)

=[(sin^2A+cos^2A)/(cosA.sinA)].[(1-sin^2A)/sinA].[(1-cos^2A)/cosA]

=(1/cosA.sinA).(cos^2A/sinA).(sin^2A/cosA)

=(1×cos^2A×sin^2A)/(cos^2A×sin^2A)

=1 , proved