Question

tan(2x-3y)tan(4y-x)=1,x,y in(0,(pi)/(2)), then the value of 2sqrt(3)tan((x+y)/(6))​

Answer 1

Correct option is

A

1−3x

2

3x−x

3

Let tan

−1

x=θ

tan2θ=(

1−x

2

2x

)

⇒tan

−1

(

1−x

2

2x

)=2θ

Then, tan

−1

y=tan

−1

x+2tan

−1

x

tan

−1

y=3tan

−1

x

⇒tan

−1

y=tan

−1

1−3x

2

3x−x

3

⇒y=

1−3x

2

3x−x

3

Hence, option A is correct.