Solve the equation `tan^(-1)2x+tan^(-1)3x=pi/4`

1.	Solve the equation `tan^(-1)2x+tan^(-1)3x=pi/4`
Answer» Correct Answer - `x = (1)/(6)` Given, `tan ^(-1) 2 x + tan ^(-1) 3x = (pi)/(4)` `rArr " " tan ^(-1) (( 2x + 3x )/( 1 - 6x^(2))) = (pi)/( 4)` `rArr " " ( 5x)/( 1- 6x ^(2)) = 1` `rArr " " 6x ^(2) + 5x - 1 = 0` `rArr " " (x + 1 ) ( 6x - 1 ) = 0` ` rArr " " x = -1 or (1)/(6)` But `x = -1 ` does not satisfy the given equation. `therefore ` We take ` x = (1)/(6)`.

Discussion

If `alpha=3sin^-1(6/11) `and `beta=3cos^-1(4/9)`, where the inverse trigonometric functions take only the principal values, then the correct option(s) is (are)A. `cos beta gt 0`B. ` sin beta lt 0`C. ` cos ( alpha + beta) gt 0`D. ` cos alpha lt 0`
if `cos^(-1)((2)/(3x))+cos^(-1)((3)/(4x))=(pi)/2, x>3/4` then `x=` (a) `(sqrt(145))/(11)` (b) `(sqrt(145))/(12)` (c) `(sqrt(146))/(10)` (d) `(sqrt(146))/(11)`A. `(sqrt ( 145))/( 10 )`B. `( sqrt ( 146))/( 12)`C. ` (sqrt ( 145))/( 12)`D. `(sqrt ( 145))/( 11)`
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Let `tan^(-1)y=tan^(-1)x+tan^(-1)((2x)/(1-x^2))`, where `|x|
Solve the equation `tan^(-1)2x+tan^(-1)3x=pi/4`
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