A) 0
B) 1
C) 2
D) 4
Correct Answer: D
Solution :
Given that, \[\cos (\alpha - \beta ) = 1\] and \[\cos (\alpha - \beta ) = 1/e\], where a, \[\alpha ,\,\beta \,\,\in \,\,\left[ -\pi ,\,\,\pi \right]\] Now, \[\cos \left( \alpha -\beta \right)= 1\,\,\Rightarrow \,\,\,\alpha -\beta =0\,\,\Rightarrow \,\,\,\alpha =\,\,\beta \] \[\therefore \,\,\,cos(\alpha +\beta )=\,\,1/e\,\,\Rightarrow \,\,cos\,\,2\alpha =1/e\] \[\therefore \,0 <1/e <1 and 2\alpha \in \left[ -2\pi ,\,\,2\pi \right]\] There will be two values of \[2\alpha \] satisfying \[\cos 2\alpha =1/e\,\,in \left[ 0,\,\,2\pi \right] and two in \left[ -\,2\pi ,\,\,0 \right].\] There will be four values of a in \[[-\,\pi ,\,\,\pi ]\] and correspondingly four values of \[\beta \]. Hence there are four sets of \[\left( \alpha ,\, \beta \right).\]You need to login to perform this action.
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