Trignometrey tan^3/ 1+tan^2 + cot^3/1+cot^2 = sec × cosec - 2 sin × cos
LHS = RHS class 10th
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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 (PROVED)
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