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 show that tan3 theta/1+tan2 theta + cot3 theta/1+cot2 theta = sec theta cosec theta - 2sin theta cos theta

Tan^3A / Sec^2A + Cot^3A / Cosec^2A 

= (sin^3A/cos^3A) / (1 / Cos^2A) + (Cos^3A/Sin^3A) / (1 / Sin^2A) 

= Sin^3A/CosA + Cos^3A/SinA 

= (Sin^4A + Cos^4A) / SinA.CosA 

= [ (Sin^2A + Cos^2A)^2 - 2Sin^2A.Cos^2A] / SinA.CosA 

= ( 1- 2Sin^A.Cos^A)/ SinA.CosA 

RHS = SecA CosecA - 2sinAcosA 

= 1/CosA . 1/SinA - 2SinACosA 

= (1 - Sin^2A.Cos^2A) / sinAcosA 

Hence LHS = RHS (PROVED)
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Xplain pls..!
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thnx!
 
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Tan^3A / Sec^2A + Cot^3A / Cosec^2A 
= (sin^3A/cos^3A) / (1 / Cos^2A) + (Cos^3A/Sin^3A) / (1 / Sin^2A) 
= Sin^3A/CosA + Cos^3A/SinA  = (Sin^4A + Cos^4A) / SinA.CosA 
= [ (Sin^2A + Cos^2A)^2 - 2Sin^2A.Cos^2A] / SinA.CosA 
= ( 1- 2Sin^A.Cos^A)/ SinA.CosA  RHS = SecA CosecA - 2sinAcosA 
= 1/CosA . 1/SinA - 2SinACosA 
= (1 - Sin^2A.Cos^2A) / sinAcosA  Hence LHS = RHS 
                                          8]
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Correct method with detail

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THANK YOU!!!!!!!!!!!!!!!!!!!!!!
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Tan^3A / Sec^2A + Cot^3A / Cosec^2A 
= (sin^3A/cos^3A) / (1 / Cos^2A) + (Cos^3A/Sin^3A) / (1 / Sin^2A) 
= Sin^3A/CosA + Cos^3A/SinA  = (Sin^4A + Cos^4A) / SinA.CosA 
= [ (Sin^2A + Cos^2A)^2 - 2Sin^2A.Cos^2A] / SinA.CosA 
= ( 1- 2Sin^A.Cos^A)/ SinA.CosA  RHS = SecA CosecA - 2sinAcosA 
= 1/CosA . 1/SinA - 2SinACosA 
= (1 - Sin^2A.Cos^2A) / sinAcosA  Hence LHS = RHS 
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ha
 
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