Prove this equation
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(1+Cot A - Cosec A) (1+TanA+SecA)
= (sinA + cosA - 1)/sinA (sinA + cosA +1)/cosA
= [(sinA + cosA)^2 - 1] /sinAcosA
= (sinA^2 + cosA^2 + 2sinAcosA - 1)/sinAcosA
= (1-1 + 2sinacosA) /sinAcosA
= 2
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Step-by-step explanation:
(1+cotA-cosecA)(1+tanA+secA)
= (1+cosA/sinA-1/sinA)(1+sinA/cosA +1/cosA)
=[( sinA+cosA-1)/sinA ]×[(cosA+sinA+1)
/cosA]
=[(sinA+cosA )^2-1]/sinAcosA
=(sin^2A+cos^2A+2sinAcosA-1)/sinAcosA
=(1+2sinAcosA-1)/sinAcosA
2sinAcosA/sinAcosA = 2
hence proved !
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