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3.Trigonometrical Ratios, Functions and Identities
hard
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
$2$
D
$4$
(IIT-2005)
Solution
(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.
Standard 11
Mathematics
