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Tan(45-A/2)+tan(45+A/2)=4/√3 then the general solution is

Tan(45-A/2)+tan(45+A/2)=4/√3 then the general solution is

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Grade:12th pass

1 Answers

Rajat
213 Points
4 years ago
tan(45+A/2) = (1+tanA/2)/(1-tanA/2)
tan(45-A/2) = (1-tanA/2)/(1+tanA/2)
Let,
tan(45+A/2) = x
So,
x + 1/x = 4/√3
Or, √3x^2-4x+√3=0
So, x = √3, 1/√3
Hence, tan(π/4+A/2) = tan (nπ+ π/3) or tan(nπ+π/6)
1) π/4+A/2 = nπ+π/3 
Or A= 2nπ+π/6
2) π/4+A/2 = nπ +π/6
Or A =2nπ-π/6
Thus option A is correct

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