MCQ
$......... K\ \ {{\sin }^{-1}}\frac{5}{13}={{\cos }^{-1}}\frac{119}{169}$ તો$K = ............$
- A$1$
- ✓$2$
- C$3$
- D$4$
ધારો કે $k sin^{-1} \frac{5}{13} = cos^{-1} \frac{119}{169} = \theta $ લેતાં,
$cos \theta = \frac{119}{169}$
$sin \frac{\theta}{2} = \sqrt{\frac{1 - cos \theta}{2}} = \sqrt{\frac{1 - 119/ 169}{2}}$
$sin \frac{\theta}{2} = \frac{5}{13}$
$\frac{\theta}{2} = sin^1 \frac{5}{13}$
$\theta = 2sin^1 \frac{5}{13}$
$\therefore \ cos^{-1} \frac{119}{169} = 2sin^{-1} \frac{5}{13}$
$k = 2$
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