Question

If $y=si{n}^{-1}x+ta{n}^{-1}x+se{c}^{-1}x$, then set of values of y is

• A. $-\frac{\pi }{2},\frac{3\pi }{4}$
  
• B. $\frac{-3\pi }{4},\frac{3\pi }{4}$
  
• C. $\frac{\pi }{4},\frac{3\pi }{4}$
  
• D. $\frac{-\pi }{4},\frac{\pi }{4}$

Answer 1

The correct option is C $\frac{\pi }{4},\frac{3\pi }{4}$


$y=si{n}^{-1}x+ta{n}^{-1}x+se{c}^{-1}x$
Domain of $si{n}^{-1}xis-1\le x\le 1$, of $ta{n}^{-1}xis-\infty <x<\infty$ of $se{c}^{-1}xisx\le -1$ or $x\ge 1$.
$\therefore$ Domain of the function is x = {- 1, 1}
$\therefore$ Value of $y=si{n}^{-1}(-1)+ta{n}^{-1}(-1)+se{c}^{-1}(-1)$
i.e., $\frac{-\pi }{2}-\frac{\pi }{4}+\pi =\frac{\pi }{4}$
and $si{n}^{-1}\left(1\right)+ta{n}^{-1}\left(1\right)+se{c}^{-1}\left(1\right)$
i.e., $\frac{\pi }{2}+\frac{\pi }{4}+0=\frac{3\pi }{4}$
Hence set of values of $y=\frac{\pi }{4},\frac{3\pi }{4}$