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If sec (alpha - 2 beta), sec alpha , sec...

If `sec (alpha - 2 beta), sec alpha , sec (alpha + 2 beta)` are in arithmetical progressin then `cos ^(2) alpha = lamda cos ^(2) beta (beta ne n pi, n in I)` the value of `lamda` is:

A

1

B

`(1)/(2)`

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
C
`2secA=sec(A2B)+Sec(A+2B)`
`(2)/(cosA)=(2cosA cos 2B)/(cos^(2)A-sin^(2)(2B))`
`cos^(2)A-sin^(2)(2B)=cos^(2)Acos 2B`
`cos^(2)A(1-cos2B)=sin^(2)(2B)`
`cos^(2)A 2 sin^(2)B=4sin^(2)cos^(2)B`
`(cos^(2)A)/(cos^(2)B)=2`
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