Question

tan- (1) 4x + tan-(1) 6x = π/4​

Answer 1

Step-by-step explanation:

Answer

tan

−1

4x+tan

−1

6x=

4

π

∵tan

−1

A+tan

−1

B=tan

−1

(

1−AB

A+B

)

∴tan

−1

(

1−24x

2

4x+6x

)=

4

π

⇒tan

−1

(

1−24x

2

10x

)=

4

π

⇒

1−24x

2

10x

=tan(

4

π

)⇒

1−24x

2

10x

=1⇒1−24x

2

=10x

⇒24x

2

+10−1=0⇒24x

2

+12x−2x−1=0

⇒12x(2x+1)−1(2x+1)=0⇒(12x−1)(2x+1)=0

⇒x=

2

−1

or x=

12

1

∵x=−

2

1

, LHS =tan

−1

(−2)+tan

−1

(−3) = negative



= RHS

∴

x=

12

1