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3.Trigonometrical Ratios, Functions and Identities
hard
यदि $\cos (\alpha - \beta ) = 1$ तथा $\cos (\alpha + \beta ) = \frac{1}{e}$, $ - \pi < \alpha ,\beta < \pi $, तो युग्म $(\alpha ,\beta )$ के कुल मान है
A
$0$
B
$1$
C
$2$
D
$4$
(IIT-2005)
Solution
$ – 2\pi < \alpha – \beta < 2\pi $
$\cos (\alpha – \beta ) = 1$
$\Rightarrow$ $\alpha – \beta = 0$
$\Rightarrow$ $\alpha = \beta $
$\cos 2\alpha = \frac{1}{e}$
एवं $ – 2\pi < 2\alpha < 2\pi $
अत: इसके चार हल हैं।
Standard 11
Mathematics
