Question

tan(1-x/1+x)=1/2tan​

Answer 1

Answer:

tan¯¹ 1-x/1+x = 1/2 tan¯¹ x, (x > 0)

2tan¯¹  (1+x / 1-x) =  tan¯¹x

tan¯¹ ( (2-2x / 2 +2x) / (1- (1-x/1+x)²) )  = tan¯¹ x

⇒ 2(1-x / 1+x) / {(1+x)² - (1-x)²} / (1+x)²

⇒ x = 2-2x / [(1+x² +2x -1-x² + 2x) / (1+x) ]

⇒ x = 2-2x / [ 4x / 1+x ]

⇒ x = 2-2x (1+x) / 4x

⇒ 2 + 2x -2x - 2x² = 4x²

⇒ 2x² + 4x² -2 = 0

⇒ 6x² - 2 = 0

⇒ 2 (3x²-1) =0

⇒3x² -1 =0

⇒ 3x² = 1

⇒ x² = 1/3

⇒ x = +- 1/√3

given that x>0

∴ x = +1/√3

Step-by-step explanation: