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cos(alpha-beta)=1a n dcos(alpha+beta)=l/...

`cos(alpha-beta)=1a n dcos(alpha+beta)=l/e ,` where `alpha,betamu in [-pi,pi]` . Number of pairs of `alpha,beta` which satisfy both the equations is 0 (b) 1 (c) 2 (d) 4

A

0

B

1

C

2

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
Since, `cos(alpha - beta) = 1`
`implies alpha - beta = 2npi`
But `-2pi lt alpha - beta lt 2 pi " "["as " alpha, beta in (-pi, pi)]`
`-2pi lt alpha - beta lt 2 pi " "["as " alpha, beta in (-pi, pi)]`
Given `cos (alpha + beta) = (1)/(e)`
`implies cos2 alpha = (1)/(e) lt 1`, which is true for four values of `alpha`. [as `-2pi lt 2alpha lt 2pi`]
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