MCQ
Principal value of $\tan ^{-1}(-1)$ :
- A$45^{\circ}$
- B$135^{\circ}$
- ✓$-45^{\circ}$
- D$-60^{\circ}$
✓
Answer
Correct option: C.
$-45^{\circ}$
(C)
Suppose $\tan ^{-1}(-1)=x$
$\therefore$ tan x = -1 = -tan $45^{\circ}$
tan x =tan $\left(-45^{\circ}\right)$ $\therefore$ x = $-45^{\circ}$
$\because$The range of principal value branch of $\tan ^{-1} x$ is
$\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$.
Hence correct option is (C).
Suppose $\tan ^{-1}(-1)=x$
$\therefore$ tan x = -1 = -tan $45^{\circ}$
tan x =tan $\left(-45^{\circ}\right)$ $\therefore$ x = $-45^{\circ}$
$\because$The range of principal value branch of $\tan ^{-1} x$ is
$\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$.
Hence correct option is (C).
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