Question

tan-1 x-3/x-4. +. tan-1 x+3/x+4. =. π/4

Answer 1

tan⁻¹(x - 3)/(x - 4) + tan⁻¹(x + 3)/(x + 4) = π/4
we know, tan⁻¹A + tan⁻¹B = tan⁻¹(A + B)/(1 - A.B)
So, tan⁻¹(x - 3)/(x - 4) + tan⁻¹(x + 3)/(x + 4) = tan⁻¹[{(x - 3)/(x - 4) + (x +3)/(x +4)}/{1 - (x -3)(x + 3)/(x - 4)(x + 4)}]
= tan⁻¹[(x -3)(x + 4) + (x + 3)(x - 4)}/{x² - 16 - x² + 9}]
= tan⁻¹[x² + x - 12 + x² - x - 12]/[-7]
= tan⁻¹[2x² - 24]/(-7)
= tan⁻¹(24 - 2x²)/7= π/4
⇒tanπ/4 = (24 - 2x² )/7
⇒7 - 24 = - 2x²
⇒x = ±√(17/2)

Answer 2

hope this help.......