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3. trignometrical ratios,functions and identities — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS3. trignometrical ratios,functions and identities1 Mark
MCQ
If $\cos (\alpha - \beta ) = 1$ and $\cos (\alpha + \beta ) = \frac{1}{e}$, $ - \pi < \alpha ,\beta < \pi $, then total number of ordered pair of $(\alpha ,\beta )$ is
  • A
    $0$
  • B
    $1$
  • C
    $2$
  • ✓
    $4$
✓

Answer

Correct option: D.
$4$
d
(d) $ - 2\pi < \alpha - \beta < 2\pi $

$\cos (\alpha - \beta ) = 1$

==> $\alpha - \beta = 0$

==> $\alpha = \beta $$\cos 2\alpha = \frac{1}{e}$

and $ - 2\pi < 2\alpha < 2\pi $

Hence, there will be four solutions.

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