Question

prove......tan a/(1+tan^2 a)+cot a/(1+cot^2 a)= sin a cos a
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Answer 1

Answer:

Step-by-step explanation:

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 

Answer 2

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