Prove that (1+tanA+secA)(1+cotA-cosecA)=2
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Step-by-step explanation:
(1+sinA/cosA+1/cosA)(1+cosA/sinA-1/sinA)
=(cosA+sinA+1/cosA)(sinA+cosA-1/sinA)
=(cosA+sinA+1)(sinA+cosA-1)/sinAcosA
=(sinA+cosA)²-1/sinAcosA
=sin²A+cos²A+2sinAcosA-1/sinAcosA
=1+2sinAcosA-1/sinAcosA
=2sinAcosA/sinAcosA
=2
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