prove that:(1+cotA-cosecA)(1+tanA+secA)=2
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We have to use the formulas :
tanA = sinA/cosA, cotA = cosA/sinA , tanAcotA = 1 and sin²A + cos²A = 1
(1+cotA-cosecA)(1+tanA+secA)
=> 1+tanA+secA+cotA+cotAtanA+cotAsecA-cosecA-cosecAtanA-cosecAsecA
=> 1+tanA+secA+cotA+1+cosecA-cosecA-secA-cosecAsecA
=> 2+tanA+cotA-cosecAsecA
=> 2+sin/cosA + cosA/sinA - 1/sinAcosA
=> (2sinAcosA+sin²A+cos²A-1)/sinAcosA
=>( 2sinAcosA+1-1)/sinAcosA
=> 2 = R.H.S.
HENCE PROVED
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