MHT CET 2018 Math Solved Paper

(c) tan−12x+tan−13x=

π

4

⇒ tan−1(

2x+3x

1−6x2

)=

π

4

⇒

5x

1−6x2

=tan‌

π

4

⇒

5x

1−6x2

=1
⇒ 5x = 1 - 6x2
⇒ 6x2 + 5x - 1 = 0
⇒ 6x2 + 6x - x - 1 = 0
⇒ 6x (x + 1) - 1(x +1) = 0
⇒ (x + 1)(6 x - 1) = 0
∴ x = -1, x =

1

6

When x =

1

6

, given equation is satisfied.
When x = -1, we get sum of two negative angles, hence discarded.
∴ x =

1

6