Cot3A. Sin3A /(cos A+ sinA)2 +tan3A .cos3A /(cosA+sinA)2= secA. CosecA-1/cosecA +secA
Answers
Cot³ASin³A /(CosA + SinA)² + Tan³A.Cos³A/(CosA + SinA)² = (SecA.CosecA - 1)/(CosecA + SecA)
Step-by-step explanation:
Cot³ASin³A /(CosA + SinA)² + Tan³A.Cos³A/(CosA + SinA)² = (SecA.CosecA - 1)/(CosecA + SecA)
LHS = Cot³ASin³A /(CosA + SinA)² + Tan³A.Cos³A/(CosA + SinA)²
= Cos³A /(CosA + SinA)² + Sin³A/(CosA + SinA)²
= (Cos³A + Sin³A)/(CosA + SinA)²
using a³ + b³ = (a + b)(a² + b² - ab)
= (CosA + SinA)(Cos²A + Sin²A - CosASinA)/(CosA + SinA)²
= (Cos²A + Sin²A - CosASinA)/(CosA + SinA)
= (1 - CosASinA)/(CosA + SinA)
DIviding numerator & Denominator by CosASinA
= (1/CosASinA - 1)/(1/SinA + 1/CosA)
= (SecACosecA - 1)/(CosecA + SecA)
= RHS
QED
Proved
Cot³ASin³A /(CosA + SinA)² + Tan³A.Cos³A/(CosA + SinA)² = (SecA.CosecA - 1)/(CosecA + SecA)
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