The value of 2cos- 1 √(2/3)-2cos- 1 â¡ (√6 + 1/2 √3) is equal to

Question

The value of 2cos- 1 √(2/3)-2cos- 1 â¡ (√6 + 1/2 √3) is equal to (A) (π /3) (B) (π /4) (C) (π /2) (D) (π /6)

Tardigrade Admin · Accepted Answer

2 cos -1(√(2/3))-2 cos -1((√6+1/2 √3)) =2 tan -1((1/√2))-2 tan -1((√3-√2/1+√6)) =2 tan -1((1/√2))-2[ tan -1 √3- tan -1 √2] =2( tan -1 (1/√2)+ tan -1 √2)-2 tan -1 √3 =π-(2 π/3)=(π/3)

Q. The value of $2 co s^{- 1} \frac{2}{3} - 2 co s^{- 1} \frac{6 + 1}{2 3}$ is equal to

$\frac{π}{3}$

$\frac{π}{4}$

$\frac{π}{2}$

$\frac{π}{6}$

$2 cos^{- 1} (\frac{2}{3}) - 2 cos^{- 1} (\frac{6 + 1}{2 3})$
$= 2 tan^{- 1} (\frac{1}{2}) - 2 tan^{- 1} (\frac{3 - 2}{1 + 6})$
$= 2 tan^{- 1} (\frac{1}{2}) - 2 [tan^{- 1} 3 - tan^{- 1} 2]$
$= 2 (tan^{- 1} \frac{1}{2} + tan^{- 1} 2) - 2 tan^{- 1} 3$
$= π - \frac{2 π}{3} = \frac{π}{3}$

Q. The value of 2cos−132​​−2cos−1⁡23​6​+1​ is equal to

3π​

4π​

2π​

6π​