If 3 sin-1((2x/1+x2)) - 4 cos-1((1-x2/1+x2)) + 2 tan-1 ((2x/1-x2)) = (π/3) where |x|

Question

If 3 sin-1((2x/1+x2)) - 4 cos-1((1-x2/1+x2)) + 2 tan-1 ((2x/1-x2)) = (π/3) where |x| < 1, then x is equal to (A) (1/√3) (B) -(1/√3) (C) √3 (D) -(√3/4)

Tardigrade Admin · Accepted Answer

The given equation is 3(2 tan-1x) - 4(2 tan-1x) + 2(2 tan-1x) = π/3 ∴ 2 tan-1x = π/3 ∴ tan-1 x = π/6 ∴ x = (1/√3)

Q. If $3 s i n^{- 1} (\frac{2 x}{1 + x ^{2}}) - 4 co s^{- 1} (\frac{1 - x ^{2}}{1 + x ^{2}}) + 2 t a n^{- 1} (\frac{2 x}{1 - x ^{2}}) = \frac{π}{3}$ where $∣ x ∣ < 1$ , then $x$ is equal to

$\frac{1}{3}$

$- \frac{1}{3}$

$3$

$- \frac{3}{4}$

The given equation is
$3 (2 t a n^{- 1} x) - 4 (2 t a n^{- 1} x) + 2 (2 t a n^{- 1} x) = π /3$
$∴ 2 t a n^{- 1} x = π /3$
$∴ t a n^{- 1} x = π /6$
$∴ x = \frac{1}{3}$

Q. If 3sin−1(1+x22x​)−4cos−1(1+x21−x2​)+2tan−1(1−x22x​)=3π​ where ∣x∣<1, then x is equal to

3​1​

−3​1​

3​

−43​​

The given equation is 3(2tan−1x)−4(2tan−1x)+2(2tan−1x)=π/3 ∴2tan−1x=π/3 ∴tan−1x=π/6 ∴x=3​1​

Q. If $3 s i n^{- 1} (\frac{2 x}{1 + x ^{2}}) - 4 co s^{- 1} (\frac{1 - x ^{2}}{1 + x ^{2}}) + 2 t a n^{- 1} (\frac{2 x}{1 - x ^{2}}) = \frac{π}{3}$ where $∣ x ∣ < 1$ , then $x$ is equal to

$\frac{1}{3}$

$- \frac{1}{3}$

$3$

$- \frac{3}{4}$

The given equation is
$3 (2 t a n^{- 1} x) - 4 (2 t a n^{- 1} x) + 2 (2 t a n^{- 1} x) = π /3$
$∴ 2 t a n^{- 1} x = π /3$
$∴ t a n^{- 1} x = π /6$
$∴ x = \frac{1}{3}$