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If Tan{(π/4)+x}+tan{(π/4)-x}=aProve that Tan^3{(π/4)+x}+tan^3{(π/4)-x}=a^3-3a

If Tan{(π/4)+x}+tan{(π/4)-x}=aProve that Tan^3{(π/4)+x}+tan^3{(π/4)-x}=a^3-3a

Grade:11

1 Answers

Sayam
49 Points
6 years ago
Tan{(π/4)+x}+tan{(π/4)-x}=a
now, Tan^3{(π/4)+x}+tan^3{(π/4)-x}=
*Tan{(π/4)+x} by applying a3+b3=(a+b)(a2-ab+b2)Tan{(π/4)+x}Tan2{(π/4)-x}-Tan2{(π/4)+x}+[Tan{(π/4)+x}+tan{(π/4)-x}][
=a[Tan2{(π/4)+x}+Tan2{(π/4)-x}-1]    
=a[[Tan{(π/4)+x}+tan{(π/4)-x}]2-3]
=a[a2-3]=a3-3a
 
 

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