Question

tan^(-1)(1+x)+tan^(-1)(1-x)=pi
find no of solutions.

Answer 1

$GOOD \: \: MORNING \:$

Tan-¹(1+x) + Tan-¹(1-x) =π/2

Tan-¹ { (1 + x + 1 - x )/ ( 1 - ( 1² - x² ) } = π/2

Becoz Tan-¹ A + Tan-¹ B =

Tan-¹{( A + B )/ ( 1 - AB ) }

Tan-¹ ( 2 / ( 1 - x² ) = π/2

{ 2 / ( 1 - x² ) } = Tan π/2

{ 2 / ( 1 - x² ) } = 1/0

( 1 - x² ) = 0

x= ±1

So, Number of solutions for this Equation is 2