Question

Find the principal solution of the equation.
sec x = $\frac{2}{\sqrt{3}}$

Answer 1

Solution:

As we know that principal value branch of sec inverse is [0,π]-{ π/2}

thus while solving the equation we must remember that sec inverse cancel sec x only if x belongs to principal value branch.

$sec \: x = \frac{2}{\sqrt{3}} \\ \\ x = {sec}^{ - 1} ( \frac{2}{ \sqrt{3} } ) \\ \\ x = {sec}^{ - 1} (sec( \frac{\pi}{6} )) \\ \\ x = \frac{\pi}{6}$

here we can remove sec and sec inverse since x belongs to [0,π]-{ π/2}

So, x = π/6