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Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions1 Mark
MCQ
If $\text{x}=\sin ^{ -1 }{ \text{K} },\text{y}=\cos ^{ -1 }\text{K}, -1\le \text{K}\le 1$, then the correct relationship is:
  • A
    $\text{x}+\text{y}=\frac{\pi}{8}$
  • B
    $\text{x}+\text{y}={2}$
  • ✓
    $\text{x}+\text{y}=\frac{\pi}{2}$
  • D
    $\text{x}+\text{y}=\frac{\pi}{8}$
✓

Answer

Correct option: C.
$\text{x}+\text{y}=\frac{\pi}{2}$
$\because \sin ^{ -1 }{ \theta } +\cos ^{ -1 }{ \theta } =\frac { \pi }{ 2 }$
$\therefore \text{x}+\text{y}=\sin ^{ -1 }{ \text{K} } +\cos ^{ -1 }{ \text{K} } =\frac { \pi }{ 2 }$

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