Show That {(cosecA)+(cosecA-1)}+ {(cosecA)+(cosecA+1)}=2sec²A
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Taking LHS
=CosecA / (CosecA-1) + CosecA / (CosecA+1)
=[CosecA(CosecA+1) + CosecA(CosecA-1)] / (CosecA-1)(CosecA+1) [Taking LCM]
= [Cosec^2A + CosecA + Cosec^2A - CosecA] / (Cosec^2A - 12)
= [Cosec^2A + CosecA + Cosec^2A - CosecA] / Cot^2A [Cosec2A-Cot^2A=1 => Cosec^2A-1=Cot^2A]
= [2Cosec^2A] / Cot^2A
= [2(1/Sin^2A)] / (Cos^2A/Sin^2A) [CosecA=1/SinA and CotA=CosA/SinA]
= [2(1/Sin^2A)] * (Sin^2A/Cos^2A)
= [2(1/Sin^2A)] * (Sin^2A/Cos^2A)
= 2(1/Cos^2A)
= 2Sec^2A
Taking LHS
=CosecA / (CosecA-1) + CosecA / (CosecA+1)
=[CosecA(CosecA+1) + CosecA(CosecA-1)] / (CosecA-1)(CosecA+1) [Taking LCM]
= [Cosec^2A + CosecA + Cosec^2A - CosecA] / (Cosec^2A - 12)
= [Cosec^2A + CosecA + Cosec^2A - CosecA] / Cot^2A [Cosec2A-Cot^2A=1 => Cosec^2A-1=Cot^2A]
= [2Cosec^2A] / Cot^2A
= [2(1/Sin^2A)] / (Cos^2A/Sin^2A) [CosecA=1/SinA and CotA=CosA/SinA]
= [2(1/Sin^2A)] * (Sin^2A/Cos^2A)
= [2(1/Sin^2A)] * (Sin^2A/Cos^2A)
= 2(1/Cos^2A)
= 2Sec^2A
balasrini25:
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