where A B are acute angels What is tan 2A B equal to ........

Quantitative Aptitude (CDS) Trignometry

$Let \: Sin(A+B)=\frac{\sqrt{3}}{2} \: and\: Cos(A+B)=\frac{\sqrt{3}}{2}$

where A,B are acute angels. What is tan(2A-B) equal to ?

1/2

$\sqrt{3}$

$\frac{1}{\sqrt{3}}$

$Sin(A+B) = \frac{\sqrt{3}}{2}$

$Sin(A+B) = Sin\, 60^{o}$

A+B = 60^o............................(1)

$Cos(B) = \frac{\sqrt{3}}{2}$

Cos(B) = Cos(30)

B= 30

Putting B= 30 in =n(1)

A + 30 = 60 = 30

tan(2A-B) = tan(2x30 - 30)

= tan 30 = 1 / $\sqrt{3}$

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