If tan -1( a+x)/a + tan -1 ( a-x)/a= pi/6, then prove that x2= 2 root3 a2 - Maths - Inverse Trigonometric Functions

Question

If tan -1( a+x)/a + tan -1 ( a-x)/a= pi/6,
then prove that x2= 2 root3 a​2

Manbar Singh · Accepted Answer

tan-1a+xa + tan-1a-xa = π6⇒tan-1a+xa + a-xa1 - a+xaa-xa = π6⇒a+xa + a-xa1 - a+xaa-xa = tanπ6⇒a+x+a-xaa2-a2+x2a2 = 13⇒2aa×a2x2 =13 ⇒x2 = 23a2

If tan -1( a+x)/a + tan -1 ( a-x)/a= pi/6, then prove that x2= 2 root3 a​2